Questions on Algebra: Probability and statistics answered by real tutors!

Tutors Answer Your Questions about Probability-and-statistics (FREE)

Question 511145: A man claims to have extrasensory perception. As a test, a fair coin is flipped 28 times, and the man is asked to predict the outcome in advance. He gets 20 out of 28 correct. What is the probability that he would have done at least this well if he had no ESP?
Click here to see answer by stanbon(75887)

Question 511222: Table 1 White Black Hispanic Asian Foreign Total
Dept.1 4 0 1 1 2 8
Dept.2 2 4 1 1 0 8
Dept. 3 1 2 3 1 1 8
Dept. 4 4 0 1 1 2 8
Dept. 5 3 2 1 0 2 8
Total 14 8 7 4 7 40

Table 2 Female Male Total
Black 6 2 8
White 6 8 14
Hispanic 3 4 7
Asian 2 2 4
Foreign 2 5 7
Total 19 21 40
Please refer to the conditional probability table or complete it first before attempting this assignment. The CEO has asked for a committee to be formed to approve and review promotions. Please list all your answers in percentages?
From Table 1, what is the probability of choosing an African American employee?
From Table 2, what is the probability of choosing an Asian female given all females?
From Table 1, what is the probability of choosing a White employee from Dept. 2 and then an Hispanic employee from Dept. 3?
From Table 2, what is the probability of choosing a Black male or Foreign male?
From Table 1, what is the probability of choosing a Foreigner or an Hispanic both from Department 5?

Click here to see answer by stanbon(75887)

Question 511339: 5. Using data from Boston, Massachusetts, a test of independence is run on the claim that ice cream sales per month and the number of car wrecks per month are independent. The claim is rejected.
Click here to see answer by stanbon(75887)

Question 511397: 1. Suppose we want to determine the (binomial) probability (p) of getting 6 heads in 13 flips of a 2-sided coin. Using Table 2 in Appendix B of the text, what values of n, x, and p would we use to look up this probability, and what would be the probability?
This is what I think I know:
n = 11
x = 6
p = .50q = 1-p = .50
I think this is the forumula I use:
11/(11-6)6 (.50)^2(.50)^5 =
I can't figure out any more or even if what I have done is correct. I need some line for line, number to number detail so I can really learn and understand this please.
Click here to see answer by stanbon(75887)

Question 511455: . For the table that follows, answer the following questions:
x y
1 1/3
2 2/3
3 1
4

- Would the correlation between x and y in the table above be positive or negative?
- Find the missing value of y in the table.
- How would the values of this table be interpreted in terms of linear regression?
- If a "line of best fit" is placed among these points plotted on a coordinate system, would the slope of this line be positive or negative?
(Points : 4)

Click here to see answer by stanbon(75887)

Question 511516: Calculate the probability of girls in a family with six children. In a family of six children, which sequence is more likely to occur?
a) BGGBGB
b)GGGGGG
c) equally likely
Click here to see answer by oberobic(2304)

Question 511531: A particular professor never dismisses class early. Let x denote the amount of time past the hour (minutes) that elapses before the professor dismisses class. Suppose that x has a uniform distribution on the interval from 0 to 10 min. The density curve is shown in the following figure.
(a) What is the probability that at most 4 min elapse before dismissal?
(b) What is the probability that between 3 and 7 min elapse before dismissal?
Click here to see answer by stanbon(75887)

Question 511381: a bag contains 8 balls of which 5 are red and 3 are white.If a man selects 2 balls at random from the bag,what is the probability that he will get one ball of each colour?
Click here to see answer by bucky(2189)

Question 511560: The weight of a astronnaut. The weight W of an object varies inversely as the square of the distance d from the center of the earth. At sea level (3978 mi from the center of the earth) an astronaut weighs 131 lbs. Find the weight when she is 198 mi above the surface of the earth and the spacecraft is not in motion. I can not figure this out for the life of me or even begin to figure out where to start can someone pls help?
Click here to see answer by scott8148(6628)

Question 511593: Consider the hypothesis test:
H o: u < 50
H a: u > 50
A. X bar = 52.5
B. x bar = 51
C. x bar = 51.8
I need help figuring the answers out and need to put them into excel.
Click here to see answer by stanbon(75887)

Question 511561: Let z denote a variable that has a standard normal distribution. Determine the value z* to satisfy the conditions below. (Round all answers to two decimal places.)
(a)P(z < z*) = 0.0244
(b)P(z < z*) = 0.0101
(c)P(z < z*) = 0.0494
(d)P(z > z*) = 0.0199
(e)P(z > z*) = 0.0101
(f)P(z > z* or z < -z*) = 0.2038
Click here to see answer by stanbon(75887)

Question 511602: If 3 out of 100 subjects are randomly selected, find the probability that they are group B and RH- (total 2 subjects), with replacement, without replacement.
Click here to see answer by stanbon(75887)

Question 511457: . Answer the following:
- If the correlation coefficient is -0.15, what is the sign of the slope of the regression line?
- As the correlation coefficient decreases from -0.85 to -0.88, do the points of the scatter plot move toward the regression line, or away from it?
Click here to see answer by richard1234(7193)

Question 511678: A coin is tossed an infinite number of times. Show that the probability that k heads are observed at the nth toss but not earlier equals..........

Click here to see answer by naseer_zia(1)

Question 511721: If the random variable z is the standard normal score and a < 0, is it true that P(z < a) < 0? Why or why not?
Click here to see answer by richard1234(7193)

Question 511793: BIG Corporation advertises that its light bulbs have a mean lifetime,mu of at least 2800 hours. Suppose that we have reason to doubt this claim and decide to do a statistical test of the claim. We choose a random sample of light bulbs manufactured by BIG and find that the mean lifetime for this sample is 2640 hours and that the sample standard deviation of the lifetimes is 650 hours. what are the Ho hypothesis and the Ha hypothesis that shouldbe used for this test?
Click here to see answer by John10(297)

Question 511835: Select the four winning numbers from 1,2,......36
Click here to see answer by stanbon(75887)

Question 511927: y=1
Click here to see answer by stanbon(75887)

Question 511927: y=1
Click here to see answer by oberobic(2304)

Question 511927: y=1
Click here to see answer by mocha(2)

Question 511894: How many ways can a chairperson and an assistant chair person be selected for a research project if there are eight scientists available?
Click here to see answer by mocha(2)

Question 511960: HOW DO YOU SOLVE (TRUE OR FALSE) " IF YOU ROLL SIX SIDED DIE SIX TIMES, YOU WILL ROLL AN EVEN NUMBER AT LEAST ONCE.
Click here to see answer by oberobic(2304)

Question 263243: A filling process is supposed to fill jars with 16 ounces of grape jelly. Specifications state that each jar must contain between 15.95 and 16.05 ounces. A jar is selected from the process every half hour until a sample of 100 jars is obtained. When the fills of the jars are measured, it is found that = 15.9750 and s = .02454. Using and s as point estimates of and , estimate the probability that a randomly selected jar will have a fill, x, that is out of specification. Assume that the process is in control and that the population of all jar fills is normally distributed.
Click here to see answer by kyungjo(1)

Question 512085: Find the area under the standard normal curve for the following:
(A) P(z < -1.80)
(B) P(-1.93 < z < 0)
(C) P(-0.17 < z < 2.05)

Click here to see answer by stanbon(75887)

Question 512128: If the probability of seeing moose in a day in a certain region of Alaska is 0.47, what is the probability of not seeing any moose in a day there?
Click here to see answer by jim_thompson5910(35256)

Question 512132: Essay; show all work. Last fall, a gardener planted 95 iris bulbs. She found that only 80 of the bulbs bloomed in the spring.

Find the empirical probability that an iris bulb of this type will bloom. Give answer as a fraction in lowest terms.
How many of the bulbs should she plant next fall if she would like at least 91 to bloom?
show your work
Click here to see answer by richard1234(7193)

Question 512249: 1. Given that there is a root of between 0.7 and 0.9. Using Regula-Falsi method determine its value correct to 5 decimal places.
Click here to see answer by richard1234(7193)

Question 512229: In order to test the hypotheses H0: p = 0.25 versus Ha: p < 0.25 for a sample of size 200, for what values of the test statistic should the null hypothesis be rejected? (Use a significance level of 0.05.)
Click here to see answer by stanbon(75887)

Question 512349: A bowl contains 27 candies. 9 are red, 6 are green, and 12 are blue. Suppose you take 3 pieces of candy without looking. What is P(E)? Round your answer to 3 decimal places.
Click here to see answer by stanbon(75887)

Question 512333: 1.) Suppose a uniform random variable can be used to describe the outcome of an experiment with outcomes ranging from 20 to 80. What is the probability that this experiment results in an outcome less than 30?
Click here to see answer by stanbon(75887)

Question 436448: The size of the sampling error is
A. Directly related to the sample size, i.e., the larger the sample size, the larger the sampling error.
B. Directly related to the population mean, i.e., the larger the mean, the larger the sampling error.
C. Inversely related to the sample size, i.e., the larger the sample size, the smaller the sampling error.
D. Inversely related to the population standard deviation, i.e., the smaller the standard deviation, the larger the sampling error.

Click here to see answer by shrestha5(1)

Question 512530: Birth weights at a local hospital have a normal distribution with a mean of 110 oz. and a standard deviation of 15 oz. What is the probability that a child born at this hospital weighs less than 7 lbs?
Click here to see answer by stanbon(75887)

Question 512818: A singer song-writer wishes to compose a melody. Each note in the melody must be one of the 14 notes in her vocal range. How many different sequences of 3 notes are possible?
Click here to see answer by richard1234(7193)

Question 512911: From a large number of actuarial exam scores, a random sample of 250 scores is selected, and it is found that 177 of these 250 are passing scores. Based on this sample, find a 90% confidence interval for the proportion of all scores that are passing. Then complete the table below.
Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places.
What is the lower limit of the 90% confidence interval?
What is the upper limit of the 90% confidence interval?
Click here to see answer by stanbon(75887)

Question 512855: If there are 5 questions and each question has two possible answers, how many different combinations of answers are there? and what are they?
Example:
1. Cheese or Knife
2. Truth or Lie
3. Water or Friend
4. Intervene or Ignore
5. Stand or Sit
I started with trying to write out all the possible combinations but that just got me more confused. the answers aren't just simple true/false either and I think that really confused me, also.
thank you! :D
Click here to see answer by stanbon(75887)

Question 512815: Studies have shown a particular television commercial is understood by 25% of first grade students and 80% of fourth grade students. If a television advertising agency randomly selects one first grader and one fourth grader, what is the probability neither child would understand the commercial, assuming the children's reactions are independent?

Click here to see answer by stanbon(75887)

Question 512920: Below are four bivariate data sets.
1.
x y
1.00 4.2
2.0 6.1
3.0 6.8
4.0 4.2
5.0 4.9
6.0 8.3
7.0 5.5
8.0 6.9
9.0 8.4
10.0 7.9
2.
u v
1.00 7.7
2.0 4.9
3.0 10.2
4.0 6.1
5.0 2.2
6.0 5.0
7.0 9.1
8.0 3.7
9.0 9.5
10.0 6.6
3.
w t
1.00 8.1
2.0 7.4
3.0 8.0
4.0 6.1
5.0 6.8
6.0 4.4
7.0 5.1
8.0 4.1
9.0 4.4
10.0 3.1
4.
m n
1.00 10.0
2.0 9.0
3.0 8.0
4.0 7.0
5.0 6.0
6.0 5.0
7.0 4.0
8.0 3.0
9.0 2.0
10.0 1.0

1. For which data set is the sample correlation coefficient r closest to 0?
a. the x, y data set
b. the u, v data set
c. the w, t data set
d. the m, n data set
e. none of these data sets
2. Which data set indicates the strongest negative linear relationship between its two variables?
a. the x, y data set
b. the u, v data set
c. the w, t data set
d. the m, n data set
e. none of these data sets
3. Which data set is the sample correlation co efficient r equal to 1?
a. the x, y data set
b. the u, v data set
c. the w, t data set
d. the m, n data set
e. none of these data sets

4. Which data set has an apparent positive, but not perfect linear relationship between its two variables?
a. the x, y data set
b. the u, v data set
c. the w, t data set
d. the m, n data set
e. none of these data sets
Click here to see answer by richard1234(7193)

Question 512965: When water flows across farm land, some of the soil is washed away, resulting in erosion. An experiment was conducted to investigate the effect of the rate of water flow on the amount of soil washed away. Flow is measured in liters per second and the eroded soil is measured in kilograms. The data are given in the following table.
Flow rate .31 .85 1.26 2.47 3.75
Eroded soil .82 1.95 2.18 3.01 6.07
The association between flow rate and amount of eroded soil is positive or negative? how so?
Click here to see answer by stanbon(75887)

Question 512927: If you are dealt 3 cards from a shuffled deck of 52 cards, what is the probability that all 3 cards are picture cards?
Click here to see answer by htmentor(1343)

Question 513084: A class has 10 males and 14 females. Two students are selected at random. What is the probability that both of the students are males?
Click here to see answer by Edwin McCravy(20054)

Question 513146: Give an example of a set of five numbers where the mode is 7
Click here to see answer by stanbon(75887)

Question 513151: Shaq is in a free throw shooting competition where he shoots exactly 20 free throws and tries to make as many as he can. The probability he makes a free throw is a constant value of 0.45. Assume his shots are independent of each other.
a. What is the expected number of free throws Shaq will make?
I did 20X0.45= 9 9 expected throws.
b. What is the mode number of free throws Shaq will make?
This is the question I am most confused on. I am not sure how to create the data I need to find the mode.
c. What is the probability Shaq makes exactly 6 free throws?
For this I used the formula and got: P(x=6)= .074
d. What is the probability Shaq makes not less than 12 free throws?
I think this is a typo on my teachers part, and I will ask and get back to you.
Thanks in advance guys!!
Click here to see answer by stanbon(75887)

Question 513143: three numbers have a mode of 5 and a total of 11.What is the range of the three numbers
Click here to see answer by stanbon(75887)

Question 513128: 5. The U.S. economy has been in a deep recession for a while. The President Obama recently has proposed a project to rescue the economy. However, according to the survey, sixty percent of Americans still believe that the project proposed by the president will have very limited effect on the economy and the country will still be in a recession in the following year. Suppose that we randomly select a sample of 20 Americans.
a. What is the probability that exactly 12 people believe that the U.S. economy will still be in a recession in the following year? (5%) (Note: without calculation process, no credit)
b. What is the probability that no more than five people believe that the U.S. economy will still be in a recession in the following year? (5%) (Note: without calculation process, no credit)
c. How many people would you expect to say the U.S. economy will still be in a recession in the following year? (5%) (Note: without calculation process, no credit)

Click here to see answer by stanbon(75887)

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