Tutors Answer Your Questions about Probability-and-statistics (FREE)
Question 139893: Can you please tell me if this is correct?
If one of the 50 shoppers surveyed is chosen at random, what is the probability that the shopper preferred either drink A or drink B? My answer would be 17/50
Drink survey
Drink A = 5 shoppers
Drink B = 12 shoppers
Drink C = 14 shoppers
Drink D = 11 shoppers
Drink E = 8 shoppers
Click here to see answer by stanbon(75887)  |
Question 139901: A student team examined parked cars in four different suburban shopping malls. One hundred vehicles were examined in each location. At a = .05, does vehicle type vary by mall location? ( Data are from a project by MBA students Steve Bennett, Alizia Morals, Steve Olson, and Geg Corda).
Vehicle Type Somerset Oakland Great Lakes Jamestown Row Total
Car 44 49 36 64 193
Minivan 21 15 18 13 67
Full Size Van 2 3 3 2 10
SUV 19 27 26 12 84
Truck 14 6 17 9 46
Col Total 100 100 100 100 400
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Question 139900: Sixty four students in an introductory college economics class were asked how many credits they had earned in college, and how certain they were about their choice of major. At a = .01, is the degree of certainty independent of credits earned?
Credits earned Very certain Somewhat certain very certain Row Total
0-9 12 8 3 23
10-59 8 4 10 22
60 or more 1 7 11 19
Col Total 21 19 24 64
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Question 139974: In a bumper test, three types of autos were deliberately crashed into a barrier at 5 mph, and the
resulting damage (in dollars) was estimated. Five test vehicles of each type were crashed, with
the results shown below. Research question: Are the mean crash damages the same for these three
vehicles? Crash1
Goliath
1600
760
880
1950
1220
Varmint
1290
1400
1390
1850
950
Weasel
1090
2100
1830
1250
1920
Click here to see answer by stanbon(75887) |
Question 139925: Can people really identify their favorite brand of cola? Volunteers tasted coca-cola classic, pepsi, Diet cola,and Diet pepsi, with the results ahawn below. At a = .05, is the correctness of the prediction different for the two types of cola drinkers? could you identify your favorite brand in this kind of test? Since it is a 2x2 table, try also a two-tailed two-sample z test for n= n2, vertify that z2 is the same as your chi square statistic, which test do you perfer? Why ( Data are from consumer Reports 56, no.8 (August 1991), p. 519.
Correct Regular cola Diet cola Row Total
Yes, got it right 7 7 14
No, got it wrong 12 20 32
Col Total 19 27 46
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Question 139922: High levels of cockpit noise in an aircraft can damage the hearing of pilots who are exposed to this hazard for many hours. Aboeing 727 co-pilot collected 61 noise observations using a handheld sound meter. Noise level is defined as "low" (under 88 decibels), "medium" (88 to 91) decibels), or "high" (92 decibels or more). There are three flight phases (climb, cruise, descent). At a = .05 is the cockpit noise level independent of flight phase? ( Data are from capt. Robert E. Hartl.
Noise level Climb Cruise Descent Row Total
Low 6 2 6 14
medium 18 3 8 29
high 1 3 14 18
col total 25 8 28 61
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Question 139919: Classic Lotto Prize Payout Table
Amount of Numbers Prize
3 $2
4 $50
5 $2000
6 Jackpot
CT Lottery is played by selecting six different numbers out of forty-four numbers on a game card (1-44). Six different numbers are drawn randomly by CT. If your selection matches all six of the states drawn numbers then you win the jackpot.
What is the probability of winning the jackpot prize?
How do I figure this out?
I think the actual answer is either 5,082,517,440 by multiplying 44x43x42x41x40x39 or it could be 7,059,052 but I don't know how to get that answer. Can you please explain to me how to do it. Thank you
Click here to see answer by stanbon(75887) |
Question 139734: Having a lot of trouble with this. Please help and show me how so I can actually learn from all this. Thanks!
PS- I am allowed to use Megastat on this so any direction there would be welcomed as well.
Q: Labor negotiators estimate that 30% of all major contract negotiations result in a strike. During the next year, 12 major contracts must be negotiatied. Show all of your work, the results below are from MegaStat.
Binomial Distribution:
N 12
P 0.3
Expected Value 3.600
Variance Standard 2.520
Deviation 1.587
A. Determine the probabiltiy of no strikes next year.
B. Determine the probabiloty of 3 or 4 strikes next year.
C. What is the average number of strikes expected for next year?
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Question 139732: Having a lot of trouble with this. Please help and show me how so I can actually learn from all this. Thanks!
PS- I am allowed to use Megastat on this so any direction there would be welcomed as well.
The bi-monthly starting salaries of recent statistician graduates follow the normal distribution with a mean of $2,625 and a standard deviation of $350. (shos all your work please)
A. What is the z-value for a salary of $2,200?
B. What is the approximate percent of statisticians making between $2,625 & $2,975?
C. What is the approximate percent of statisticians making between $2,275 & $2,625?
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Question 139730: Having a lot of trouble with this. Please help and show me how so I can actually learn from all this. Thanks!
Occurrences
0
1
2
Probability
0.60
0.30
0.10
#1 Compute the mean number of the incidents
#2 Compute the variance for this distribution
PS- I am allowed to use Megastat on this so any direcetion there would be welcomed as well.
Click here to see answer by stanbon(75887) |
Question 139972: You roll two standard dice and multiply the results. What is the probability that the product is odd?
b)You roll three standard dice and add the results. What is the probability that the sum is at most 4?
thankyou so much for your time. Bill
Click here to see answer by checkley77(12844) |
Question 139725: IQ scores have a normal distribution with a mean of 100 and a standard deviation of 15. What two IQs seperate the middle 90 percent from the remainder of the distribution?
part of my answer is: 90 - 100 / 15 = 0.66
and the second part is what i am having trouble with
Click here to see answer by stanbon(75887) |
Question 139546: help..
2. For the ANOVA table below, answer each question.
A. How many treatments (groupings) are being compared?
B. How many total observations are in this analysis?
C. What is the hypothesis tested here?
Source DF Sum of Squares Mean Square F Ratio Prob>F
ID 2 49.38620 24.6931 1.4837 0.2415
Error 33 549.20797 16.6427
C. Total 35 598.59417
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Question 139473: need help please.....
For the ANOVA table below, answer each question.
Source DF Sum of Squares Mean Square F Ratio Prob>F
ID 2 49.38620 24.6931 1.4837 0.2415
Error 33 549.20797 16.6427
C. Total 35 598.59417
A. How many treatments (groupings) are being compared?
B. How many total observations are in this analysis?
C. What is the hypothesis tested here?
Click here to see answer by stanbon(75887) |
Question 140064: There are two spinners. The first spinner is a circle that is cut in fours. the numbers read 10, 12, 14, 18. The other spinner is also cut in fours and the numbers are 1, 2, 3, 4
Ok.. The two spinners shown are spun and the difference between the results is found. Find the probability that the difference is a multiple of 3.
Thankyou.. Danielle, AKA Dani
Click here to see answer by mathslover(157)  |
Question 140048: I pick up 3 cards from a standard deck, one after another, keeping each card that I pick (without replacement) What is the probability that as least 2 of the 3 cards are the same suit?
B) There are 10 cards in a hat, 4 red and the rest black. You pull out 2 cards without looking. What is the probability that they are the same color? Would this be (Prob of red)= 4/10*3/9+(Prob of all black) 6/10*5/9=42/90= 46%
Click here to see answer by stanbon(75887) |
Question 140091: HELP! I have tried several different ways to set up this problem, but I can't get it right! I don't know what formula to use in order to solve it.
Melinda’s lights went out. She has 3 pairs of red socks in her drawer, 2 pairs of black socks, and 5 pairs of white socks. What is the minimum number of pairs she must remove from the drawer to ensure that she has a pair of each color?
Thank you!
Click here to see answer by scott8148(6628)  |
Question 140104: In a bumper test, three types of autos were deliberately crashed into a barrier at 5 mph, and the resulting damage (in dollars) was estimated. Five test vehicles of each type were crashed, with the results shown below. Research question: Are the mean crash damages the same for these three vehicles? Crash1
Crash Damage ($)
Goliath Varmint Weasel
1,600 1,290 1,090
760 1,400 2,100
880 1,390 1,830
1,950 1,850 1,250
1,220 950 1,920
Click here to see answer by stanbon(75887) |
Question 140268: In order to test whether marathon races are bad for health, a researcher took a random sample of 400 runners who participated in the New York half marathon, and found that 13% of them got sick in the two-week period after the marathon. In a second sample of 400 runners who did not participate in the marathon, only 3% were sick in the same two week period. What would be the null hypothesis? Find a 90% confidence interval for the percentage of New York half marathon runners who got sick in the two weeks after the race.
PLS pls help, I am only a student in long distance education and need help to solve exam problems. This is from my question paper
Click here to see answer by stanbon(75887) |
Question 140267: To see whether silicon chip sales are independent of where the US economy is in the business cycle, data have been calculated on the weekly sales of a firm and on whether the US economy was rising to a cycle peak, at a cycle peak, falling to a cycle peak or at a cycle trough. The results are
Weekly Chip Sale
HIGH MEDIUM LOW TOTAL
Economy at peak 20 7 3 30
Economy at trough 30 40 30 100
Economy rising 20 8 2 30
Economy Falling 30 5 5 40
TOTAL 100 60 40 200
State the null hypothesis. At 0.10 significance level, what is your conclusion?
Given the tabulated value of test statistic is 10.645
Pls hlep. I am student from long distance education and these are the kind of questions that come for my exam
Click here to see answer by stanbon(75887) |
Question 140263: Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The executives hire a statistical consultant and ask her to determine the mean shopping time, , of customers at the supermarkets. The consultant will collect a random sample of shopping times at the supermarkets and use the mean of these shopping times to estimate . Assuming that the standard deviation of the population of shopping times at the supermarkets is minutes, what is the minimum sample size she must collect in order for her to be confident that her estimate is within minutes of ?
Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).
(If necessary, consult a list of formulas.)
Click here to see answer by stanbon(75887) |
Question 140266: The members of a consulting firm rent cars from three rental agencies:
60% from Agency 1, 30 % from Agency 2 and 10% from Agency 3. If 9% of the cars from Agency 1 need a tune-up, 20 % of the cars from agency 2 need a tune up and 6% of the cars from agency 3 need a tune-up, what is the probability that a rental car delivered to the firm will need a tune -up?
Pls help as I am student from long distance education and unable to solve this...
Click here to see answer by stanbon(75887) |
Question 140256: The following hypotheses is an example of
H0:π ≤.40
Ha:π > .40
a a one tail test for means
b. a two tail test for means
c. A one tail test for proportions
d. a two tail for proportions
e. None of the above
Click here to see answer by stanbon(75887) |
Question 140262: 1.Of the following ordinary words, which one is most closely associated with the meaning of a hypothesis?
a. trial
b. decision
c. outcome
d. assumption
2.The appropriate null hypothesis for an upper-tail test to determine if mean body weight of all the men who have joined a health club exceeds 185 pounds would be
a. HO: u = 185 lb.
b. HO: u > 185 lb.
c. HO: u less than or = to 185 lb
d. HO: u not = to 185 lb
3.The test statistic that is used to test hypotheses about the mean when a small sample is involved follows a _________ distribution.
a. t
b. z
c. chi-square
d. binomial
Use the following scenario for questions 4 – 6
Easy Eye, Inc. manufactures adult sunglasses of all types. The company’s management is not sure whether to target the next promotional campaign primarily toward men or women and has asked the research team to determine whether the market for sunglasses is split in half. A study is conducted at various cooperating stores selling sunglasses scattered throughout the market area. In a random sample of 300 adult purchasers of sunglasses, 141 were men.
4.If pi is the proportion of adult sunglass purchasers who are men, what is the appropriate null hypothesis for Easy Eye, Inc. to test?
a. H0: pi = 0.5
b. H0: pi is not = to 0.5
c. H0: pi greater than or = to 0.5
d. H0: pi less than or = to 0.5
5.What is the value of the test statistic?
a. –0.06
b. –0.50
c. –1.04
d. –2.54
6.Based on the data and at alpha = 0.05, what can Easy Eye’s management conclude?
a. An equal proportion of men and women are buying sunglasses in the market area.
b. A greater proportion of women buy sunglasses than do men in the market area.
c. A greater proportion of men buy sunglasses than do women in the market area.
d. There is not an equal proportion of men and women buying sunglasses in the market area.
7.Sherry Weinstein, a buyer, has decided that she will spend an extra $7 per shirt for the next 10,000 T-shirts she buys for her chain of stores only if the vendor of the more expensive shirt can show conclusive evidence that its shirt can withstand at least 20 more times in the wash without fading. The vendor elected to set u1 as the mean number of washes without fading for the more expensive shirt. An appropriate null hypothesis for the vendor to test is
a. H0: u1 – u2 less than or = to 20.
b. H0: u1 – u2 < 20
c. H0: u1 – u2 > 20.
d. H0: u1 – u2 greater than or = to 0
8.The technique that is used to determine if more than two population means are equal by analyzing the variation in the data is known as
a. chi-square.
b. analysis of variance.
c. correlation analysis.
d. least squares regression.
9.The least squares method finds the equation of the line that __________ the __________ of the squared deviations between the points and the line.
a. maximizes, sum
b. minimizes, product
c. minimizes, sum
d. maximizes, product
10.A linear regression between Y and X produced the following equation for the least squares line:
y(with a little upside v over it) = 2.15 – 3.2x
Which of the following statements concerning this relationship is true?
a. For every one-unit increase in X, Y increases 3.2 units.
b. For every one-unit increase in Y, X decreases 3.2 units.
c. For every one-unit increase in X, Y decreases 3.2 units.
d. For every one-unit increase in Y, X increases 3.2 units.
11.Horace Mann, principal of Jones Public School, has decided to construct a time series model to obtain a 2- and a 3-period moving average to forecast student enrollments for next term. Which statement is true concerning the accuracy of each forecast that Horace will obtain?
a. The 2-period forecast will be more accurate than the 3-period forecast.
b. The 3-period forecast will be more accurate than the 2-period forecast.
c. Both forecasts will be equally accurate.
d. Either forecast could be more accurate than the other.
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Question 140135: If I have a normal distribution that has a mean of 100 and standard deviation of 20, and if I draw a sample of size n=40, how do I find the probability that all the 40 sampled values are less than 120? The 40 values being sampled are done so without replacement.
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Question 140327: please help solve: I have a deck of 52 cards. All red cards have been removed from the deck. Remaining cards have been shuffle.
select a card from the remaining deck. Do not replace the card. Select another card. What is the probability that a red three is selected and a face card is selected.
my answer is 0.
there are no red cards in the deck?
But what about the face card???
Click here to see answer by stanbon(75887) |
Question 140366: A quiz with 4 multiple choice questions, each with 3 choices, was given. A student needs either 3 or 4 right to pass the quiz, but is totally clueless like myself. What is the probability of passing by pure guesswork? I wonder if my teacher made this problem up to make fun of me? :(.. thankyou Shelly
Click here to see answer by scott8148(6628) |
Question 140324: Please help solve.
I have a deck of 52 cards. all the face cards have been removed from the deck, which is 12 cards. Select 3 cards from the pile of 12 cards. for each question.
How many ways are there of selecting one of each facecard from the pile, is it combination or permutation and why.
How many ways are there of selecting three of the same face cards ( 3 kings, 3 jacks, 3 queen) from the pile. Combination or permutation and why
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Question 140360: Hello, I a sorry to be inquiring help from you but this is a hard subject for me. I have includewhat I believe the answers are but I don't trust my own answers. Please help:
Sherry Weinstein, a buyer, has decided that she will spend an extra $7 per shirt for the next 10,000 T-shirts she buys for her chain of stores only if the vendor of the more expensive shirt can show conclusive evidence that its shirt can withstand at least 20 more times in the wash without fading. The vendor elected to set m1 as the mean number of washes without fading for the more expensive shirt. An appropriate null hypothesis for the vendor to test is
a. H0: m1 – m2£ 20.
b. H0: m1 – m2 < 20
c. H0: m1 – m2 > 20. (I chose c)
d. H0: m1 – m2£ 0
The technique that is used to determine if more than two population means are equal by analyzing the variation in the data is known as
a. chi-square.
b. analysis of variance.
c. correlation analysis. (I chose c)
d. least squares regression.
The least squares method finds the equation of the line that __________ the __________ of the squared deviations between the points and the line.
a. maximizes, sum
b. minimizes, product
c. minimizes, sum
d. maximizes, product (I picked d)
Thanks for your help.
Click here to see answer by stanbon(75887) |
Question 140428: A spinner is made with twelve 30 degree sectors and is numbered 1 to 12. It is spun twice and the results are added. What is the probability that the sum is larger than 16? If the spinner is spun three times, what is the probability that the sum of the three results is 6 or below?
This is a confusing question. Kelly
Click here to see answer by scott8148(6628) |
Question 140488: Two-Sample T-Test
We want to know whether the means of two populations on some outcome differ. For example, we want to compare two categories of males and females two populations’ age difference in purchasing concert tickets. The two-sample t-test is a hypothesis test for answering questions about the mean where the data are collected from two random samples of independent observations, each from an underlying normal distribution:
The steps of conducting a two-sample t-test are quite similar to those of the one-sample test. And for the sake of consistency, we will focus on another example dealing with ages of ticket purchase.
Returning to the two-sample t-test, the steps to conduct the test are similar to those of the one- sample test.
Establish hypotheses
The first step to examining this question is to establish the specific hypotheses we wish to examine. Specifically, we want to establish a null hypothesis and an alternative hypothesis to be evaluated with data.
In this case:
• Null hypothesis is that the difference between the two groups is 0. Another way of stating the null hypothesis is that the difference between the mean of the treatment group of ages for ticket purchasers and the mean of the men and women who purchase tickets is zero.
Calculate test statistic
Calculation of the test statistic requires three components:
1. The average of both sample (observed averages)
Statistically, we represent these as
2. The standard deviation (SD) of both averages
Statistically, we represent these as
3. The number of observations in both populations, represented as
From hospital records, we obtain the following values for these components:
men women
Average age 29.87 31.67
SD 8.45 8.10
n 15 15
With these pieces of information, we calculate the following statistic, t:
Use this value to determine p-value
Having calculated the t-statistic, compare the t-value with a standard table of t-values to determine whether the t-statistic reaches the threshold of statistical significance.
With a t-score -1.80 not significant, the p-value is 0.7218, a score that forms our basis to reject the null hypothesis and conclude that the age data for both male and female who purchase tickets are not 34.
Click here to see answer by stanbon(75887) |
Question 140653: 12.50
In the following regression, X = total assets ($ billions), Y = total revenue ($ billions), and n = 64
large banks. (a) Write the fitted regression equation. (b) State the degrees of freedom for a two tailed
test for zero slope, and use Appendix D to find the critical value at α = .05. (c) What is your
conclusion about the slope? (d) Interpret the 95 percent confidence limits for the slope. (e) Verify
that F = t2 for the slope. (f) In your own words, describe the fit of this regression.
R2 0.519
Std. Error 6.977
n 64
ANOVA table
Source SS df MS F p-value
Regression 3,260.0981 1 3,260.0981 66.97 1.90E-11
Residual 3,018.3339 62 48.6828
Total 6,278.4320 63
Regression output confidence interval
variables coefficients std. error t (df = 62) p-value 95% lower 95% upper
Intercept 6.5763 1.9254 3.416 .0011 2.7275 10.4252
X1 0.0452 0.0055 8.183 1.90E-11 0.0342 0.0563
14.16
(a) Plot the data on U.S. general aviation shipments. (b) Describe the pattern and discuss possible
causes. (c) Would a fitted trend be helpful? Explain. (d) Make a similar graph for 1992–2003 only.
Would a fitted trend be helpful in making a prediction for 2004? (e) Fit a trend model of your
choice to the 1992–2003 data. (f) Make a forecast for 2004, using either the fitted trend model or
a judgment forecast. Why is it best to ignore earlier years in this data set?
U.S. Manufactured General Aviation Shipments, 1966–2003
Year Planes Year Planes Year Planes Year Planes
1966 15,587 1976 15,451 1986 1,495 1996 1,053
1967 13,484 1977 16,904 1987 1,085 1997 1,482
1968 13,556 1978 17,811 1988 1,143 1998 2,115
1969 12,407 1979 17,048 1989 1,535 1999 2,421
1970 7,277 1980 11,877 1990 1,134 2000 2,714
1971 7,346 1981 9,457 1991 1,021 2001 2,538
1972 9,774 1982 4,266 1992 856 2002 2,169
1973 13,646 1983 2,691 1993 870 2003 2,090
1974 14,166 1984 2,431 1994 881
1975 14,056 1985 2,029 1995 1,028
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Question 140651: For the following question, each part of the question is worth 8 points.
A researcher wants to determine whether the number of minutes adults spend online per day is related to gender. A random sample of 315 adults was selected and the results are shown below. Test the claim that the number of minutes spent online per day is related to gender. Use α=0.05.
Minutes Spent Online Per Day
Gender 0 – 30 30 – 60 60 – 90 90 or over
Male 25 35 75 45
Female 30 45 45 15
a) Write the null and alternative hypotheses to test the claim that the number of minutes spent online per day is related to gender.
b) Show how you would calculate the expected number of males to spend 60-90 minutes online. Do not carry out the calculations. However, show how you would calculate the expected value.
c) How many degrees of freedom should you use to determine the critical value? Explain how you arrived at that number of degrees of freedom.
d) Suppose that the value of the χ2 test statistic is 18.14 and suppose that the critical value is 7.815. What conclusion would draw about the null hypothesis? Explain what numbers you are comparing to decide whether to reject or fail to reject the null hypothesis.
e) State your conclusion in terms of the original claim and indicate why you are justified in making this conclusion.
Click here to see answer by stanbon(75887) |
Question 140714: In the following regression, X = weekly pay, Y = income tax withheld, and n = 35 McDonald’s employees. (a) Write the fitted regression equation. (b) State the degrees of freedom for a two tailed test for zero slope, and use Appendix D to find the critical value at α = .05. (c) What is your conclusion about the slope? (d) Interpret the 95 percent confidence limits for the slope. (e) Verify that F = t2 for the slope. (f) In your own words, describe the fit of this regression.
R2 0.202
Std. Error 6.816
n 35
ANOVA table
Source SS df MS F p-value
Regression 387.6959 1 387.6959 8.35 .0068
Residual 1,533.0614 33 46.4564
Total 1,920.7573 34
Regression output confidence interval
variables coefficients std. error t (df = 33) p-value 95% lower 95% upper
Intercept 30.7963 6.4078 4.806 .0000 17.7595 43.8331
Slope 0.0343 0.0119 2.889 .0068 0.0101 0.0584
Click here to see answer by stanbon(75887) |
Question 140734: Easy Eye, Inc. manufactures adult sunglasses of all types. The company’s management is not sure whether to target the next promotional campaign primarily toward men or women and has asked the research team to determine whether the market for sunglasses is split in half. A study is conducted at various cooperating stores selling sunglasses scattered throughout the market area. In a random sample of 300 adult purchasers of sunglasses, 141 were men.
If "Pi" is the proportion of adult sunglass purchasers who are men, what is the appropriate null hypothesis for Easy Eye, Inc. to test?
a. H0: Pi = 0.5
b. H0: Pi "not equal to" 0.5
c. H0: Pi >= 0.5
d. H0: Pi <= 0.5
What is the value of the test statistic?
a. –0.06
b. –0.50
c. –1.04
d. –2.54
Based on the data and at "a" = 0.05, what can Easy Eye’s management conclude?
a. An equal proportion of men and women are buying sunglasses in the market area.
b. A greater proportion of women buy sunglasses than do men in the market area.
c. A greater proportion of men buy sunglasses than do women in the market area.
d. There is not an equal proportion of men and women buying sunglasses in the market area.
Click here to see answer by stanbon(75887) |
Question 140732: The appropriate null hypothesis for an upper-tail test to determine if mean body weight of all the men who have joined a health club exceeds 185 pounds would be
a. HO: u = 185 lb.
b. HO: u > 185 lb.
c. HO: u <= 185 lb
d. HO: u "not equal to" 185 lb
Click here to see answer by stanbon(75887) |
Question 140779: 9.62 The Web-based company Oh Baby! Gifts has a goal of processing 95 percent of its orders on the
same day they are received. If 485 out of the next 500 orders are processed on the same day, would
this prove that they are exceeding their goal, using α = .025? (See story.news.yahoo.com accessed
June 25, 2004.)
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020, 16021..16065, 16066..16110, 16111..16155, 16156..16200, 16201..16245, 16246..16290, 16291..16335, 16336..16380, 16381..16425, 16426..16470, 16471..16515, 16516..16560, 16561..16605, 16606..16650, 16651..16695, 16696..16740, 16741..16785, 16786..16830, 16831..16875, 16876..16920, 16921..16965, 16966..17010, 17011..17055, 17056..17100, 17101..17145, 17146..17190, 17191..17235, 17236..17280, 17281..17325, 17326..17370, 17371..17415, 17416..17460, 17461..17505, 17506..17550, 17551..17595, 17596..17640, 17641..17685, 17686..17730, 17731..17775, 17776..17820, 17821..17865, 17866..17910, 17911..17955, 17956..18000, 18001..18045, 18046..18090, 18091..18135, 18136..18180, 18181..18225, 18226..18270, 18271..18315, 18316..18360, 18361..18405, 18406..18450, 18451..18495, 18496..18540, 18541..18585, 18586..18630, 18631..18675, 18676..18720, 18721..18765, 18766..18810, 18811..18855, 18856..18900, 18901..18945, 18946..18990, 18991..19035, 19036..19080, 19081..19125, 19126..19170, 19171..19215, 19216..19260, 19261..19305, 19306..19350, 19351..19395, 19396..19440, 19441..19485, 19486..19530, 19531..19575, 19576..19620, 19621..19665, 19666..19710, 19711..19755, 19756..19800, 19801..19845, 19846..19890, 19891..19935, 19936..19980, 19981..20025, 20026..20070, 20071..20115, 20116..20160, 20161..20205, 20206..20250, 20251..20295, 20296..20340, 20341..20385, 20386..20430, 20431..20475, 20476..20520, 20521..20565, 20566..20610, 20611..20655, 20656..20700, 20701..20745, 20746..20790, 20791..20835, 20836..20880, 20881..20925, 20926..20970, 20971..21015, 21016..21060, 21061..21105, 21106..21150, 21151..21195, 21196..21240, 21241..21285, 21286..21330, 21331..21375, 21376..21420, 21421..21465, 21466..21510, 21511..21555, 21556..21600, 21601..21645, 21646..21690, 21691..21735, 21736..21780, 21781..21825, 21826..21870, 21871..21915, 21916..21960, 21961..22005, 22006..22050, 22051..22095, 22096..22140, 22141..22185, 22186..22230, 22231..22275, 22276..22320, 22321..22365, 22366..22410, 22411..22455, 22456..22500, 22501..22545, 22546..22590, 22591..22635, 22636..22680, 22681..22725, 22726..22770, 22771..22815, 22816..22860, 22861..22905, 22906..22950, 22951..22995, 22996..23040, 23041..23085, 23086..23130, 23131..23175, 23176..23220, 23221..23265, 23266..23310, 23311..23355, 23356..23400, 23401..23445, 23446..23490, 23491..23535, 23536..23580, 23581..23625, 23626..23670, 23671..23715, 23716..23760, 23761..23805, 23806..23850, 23851..23895, 23896..23940, 23941..23985, 23986..24030, 24031..24075, 24076..24120, 24121..24165, 24166..24210, 24211..24255, 24256..24300, 24301..24345, 24346..24390, 24391..24435, 24436..24480, 24481..24525, 24526..24570, 24571..24615, 24616..24660, 24661..24705, 24706..24750, 24751..24795, 24796..24840, 24841..24885, 24886..24930, 24931..24975, 24976..25020, 25021..25065, 25066..25110, 25111..25155, 25156..25200, 25201..25245, 25246..25290, 25291..25335, 25336..25380, 25381..25425, 25426..25470, 25471..25515, 25516..25560, 25561..25605, 25606..25650, 25651..25695, 25696..25740, 25741..25785, 25786..25830, 25831..25875, 25876..25920, 25921..25965, 25966..26010, 26011..26055, 26056..26100, 26101..26145, 26146..26190, 26191..26235, 26236..26280, 26281..26325, 26326..26370, 26371..26415, 26416..26460, 26461..26505, 26506..26550, 26551..26595, 26596..26640, 26641..26685, 26686..26730, 26731..26775, 26776..26820, 26821..26865, 26866..26910, 26911..26955, 26956..27000, 27001..27045, 27046..27090, 27091..27135, 27136..27180, 27181..27225, 27226..27270, 27271..27315, 27316..27360, 27361..27405, 27406..27450, 27451..27495, 27496..27540, 27541..27585, 27586..27630, 27631..27675, 27676..27720, 27721..27765, 27766..27810, 27811..27855, 27856..27900, 27901..27945, 27946..27990, 27991..28035, 28036..28080, 28081..28125, 28126..28170, 28171..28215, 28216..28260, 28261..28305, 28306..28350, 28351..28395, 28396..28440, 28441..28485, 28486..28530, 28531..28575, 28576..28620, 28621..28665, 28666..28710, 28711..28755, 28756..28800, 28801..28845, 28846..28890, 28891..28935, 28936..28980, 28981..29025, 29026..29070, 29071..29115, 29116..29160, 29161..29205, 29206..29250, 29251..29295, 29296..29340, 29341..29385, 29386..29430, 29431..29475, 29476..29520, 29521..29565, 29566..29610, 29611..29655, 29656..29700, 29701..29745, 29746..29790, 29791..29835, 29836..29880, 29881..29925, 29926..29970, 29971..30015, 30016..30060, 30061..30105, 30106..30150, 30151..30195, 30196..30240, 30241..30285, 30286..30330, 30331..30375, 30376..30420, 30421..30465, 30466..30510, 30511..30555, 30556..30600, 30601..30645, 30646..30690, 30691..30735, 30736..30780, 30781..30825, 30826..30870, 30871..30915, 30916..30960, 30961..31005, 31006..31050, 31051..31095, 31096..31140, 31141..31185, 31186..31230, 31231..31275, 31276..31320, 31321..31365, 31366..31410, 31411..31455, 31456..31500, 31501..31545, 31546..31590, 31591..31635, 31636..31680, 31681..31725, 31726..31770, 31771..31815, 31816..31860, 31861..31905, 31906..31950, 31951..31995, 31996..32040, 32041..32085, 32086..32130, 32131..32175, 32176..32220, 32221..32265, 32266..32310, 32311..32355, 32356..32400, 32401..32445, 32446..32490, 32491..32535, 32536..32580, 32581..32625, 32626..32670, 32671..32715, 32716..32760, 32761..32805, 32806..32850, 32851..32895, 32896..32940, 32941..32985, 32986..33030, 33031..33075, 33076..33120, 33121..33165, 33166..33210, 33211..33255, 33256..33300, 33301..33345, 33346..33390, 33391..33435, 33436..33480, 33481..33525, 33526..33570, 33571..33615, 33616..33660, 33661..33705, 33706..33750, 33751..33795, 33796..33840, 33841..33885, 33886..33930, 33931..33975, 33976..34020, 34021..34065, 34066..34110, 34111..34155, 34156..34200, 34201..34245, 34246..34290, 34291..34335, 34336..34380, 34381..34425, 34426..34470, 34471..34515, 34516..34560, 34561..34605, 34606..34650, 34651..34695, 34696..34740, 34741..34785, 34786..34830, 34831..34875, 34876..34920, 34921..34965, 34966..35010, 35011..35055, 35056..35100, 35101..35145, 35146..35190, 35191..35235, 35236..35280, 35281..35325, 35326..35370, 35371..35415, 35416..35460, 35461..35505, 35506..35550, 35551..35595, 35596..35640, 35641..35685, 35686..35730, 35731..35775, 35776..35820, 35821..35865, 35866..35910, 35911..35955, 35956..36000, 36001..36045, 36046..36090, 36091..36135, 36136..36180, 36181..36225, 36226..36270, 36271..36315, 36316..36360, 36361..36405, 36406..36450, 36451..36495, 36496..36540, 36541..36585, 36586..36630, 36631..36675, 36676..36720, 36721..36765, 36766..36810, 36811..36855, 36856..36900, 36901..36945, 36946..36990, 36991..37035, 37036..37080, 37081..37125, 37126..37170, 37171..37215, 37216..37260, 37261..37305, 37306..37350, 37351..37395, 37396..37440, 37441..37485, 37486..37530, 37531..37575, 37576..37620, 37621..37665, 37666..37710, 37711..37755, 37756..37800, 37801..37845, 37846..37890, 37891..37935, 37936..37980, 37981..38025, 38026..38070, 38071..38115, 38116..38160, 38161..38205, 38206..38250, 38251..38295, 38296..38340, 38341..38385, 38386..38430, 38431..38475, 38476..38520, 38521..38565, 38566..38610, 38611..38655, 38656..38700, 38701..38745, 38746..38790, 38791..38835, 38836..38880, 38881..38925, 38926..38970, 38971..39015, 39016..39060, 39061..39105, 39106..39150, 39151..39195, 39196..39240, 39241..39285, 39286..39330, 39331..39375, 39376..39420, 39421..39465, 39466..39510, 39511..39555, 39556..39600, 39601..39645, 39646..39690, 39691..39735, 39736..39780, 39781..39825, 39826..39870, 39871..39915, 39916..39960, 39961..40005, 40006..40050, 40051..40095, 40096..40140, 40141..40185, 40186..40230, 40231..40275, 40276..40320, 40321..40365, 40366..40410, 40411..40455, 40456..40500, 40501..40545, 40546..40590, 40591..40635, 40636..40680, 40681..40725, 40726..40770, 40771..40815, 40816..40860, 40861..40905, 40906..40950, 40951..40995, 40996..41040, 41041..41085, 41086..41130, 41131..41175, 41176..41220, 41221..41265, 41266..41310, 41311..41355, 41356..41400, 41401..41445, 41446..41490, 41491..41535, 41536..41580, 41581..41625, 41626..41670, 41671..41715, 41716..41760, 41761..41805, 41806..41850, 41851..41895, 41896..41940, 41941..41985, 41986..42030, 42031..42075, 42076..42120, 42121..42165, 42166..42210, 42211..42255, 42256..42300, 42301..42345, 42346..42390, 42391..42435, 42436..42480, 42481..42525, 42526..42570, 42571..42615, 42616..42660, 42661..42705, 42706..42750, 42751..42795, 42796..42840, 42841..42885, 42886..42930, 42931..42975, 42976..43020, 43021..43065, 43066..43110, 43111..43155, 43156..43200, 43201..43245, 43246..43290, 43291..43335, 43336..43380, 43381..43425, 43426..43470, 43471..43515, 43516..43560, 43561..43605, 43606..43650, 43651..43695, 43696..43740, 43741..43785, 43786..43830, 43831..43875, 43876..43920, 43921..43965, 43966..44010, 44011..44055, 44056..44100, 44101..44145, 44146..44190, 44191..44235, 44236..44280, 44281..44325, 44326..44370, 44371..44415, 44416..44460, 44461..44505, 44506..44550, 44551..44595, 44596..44640, 44641..44685, 44686..44730, 44731..44775, 44776..44820, 44821..44865, 44866..44910, 44911..44955, 44956..45000, 45001..45045, 45046..45090, 45091..45135, 45136..45180, 45181..45225, 45226..45270, 45271..45315, 45316..45360, 45361..45405, 45406..45450, 45451..45495, 45496..45540, 45541..45585, 45586..45630, 45631..45675, 45676..45720, 45721..45765, 45766..45810, 45811..45855, 45856..45900, 45901..45945, 45946..45990, 45991..46035, 46036..46080, 46081..46125, 46126..46170, 46171..46215, 46216..46260, 46261..46305, 46306..46350, 46351..46395, 46396..46440, 46441..46485, 46486..46530, 46531..46575, 46576..46620, 46621..46665, 46666..46710, 46711..46755, 46756..46800, 46801..46845, 46846..46890, 46891..46935, 46936..46980, 46981..47025, 47026..47070, 47071..47115, 47116..47160, 47161..47205, 47206..47250, 47251..47295, 47296..47340, 47341..47385, 47386..47430, 47431..47475, 47476..47520, 47521..47565, 47566..47610, 47611..47655, 47656..47700, 47701..47745, 47746..47790, 47791..47835, 47836..47880, 47881..47925, 47926..47970, 47971..48015, 48016..48060, 48061..48105, 48106..48150, 48151..48195, 48196..48240, 48241..48285, 48286..48330, 48331..48375, 48376..48420, 48421..48465, 48466..48510, 48511..48555, 48556..48600, 48601..48645, 48646..48690, 48691..48735, 48736..48780, 48781..48825, 48826..48870, 48871..48915, 48916..48960, 48961..49005, 49006..49050, 49051..49095, 49096..49140, 49141..49185, 49186..49230, 49231..49275, 49276..49320, 49321..49365, 49366..49410, 49411..49455, 49456..49500, 49501..49545, 49546..49590, 49591..49635, 49636..49680, 49681..49725, 49726..49770, 49771..49815, 49816..49860, 49861..49905, 49906..49950, 49951..49995, 49996..50040, 50041..50085, 50086..50130, 50131..50175, 50176..50220, 50221..50265, 50266..50310, 50311..50355, 50356..50400, 50401..50445, 50446..50490, 50491..50535, 50536..50580, 50581..50625, 50626..50670, 50671..50715, 50716..50760, 50761..50805, 50806..50850, 50851..50895, 50896..50940, 50941..50985, 50986..51030, 51031..51075, 51076..51120, 51121..51165, 51166..51210, 51211..51255, 51256..51300, 51301..51345
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