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

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

Question 1153175: The class average on a statistics test is 65 marks with a standard deviation of 12 marks. What minimum mark must a student obtain to be in the top 8% of the class?
Click here to see answer by rothauserc(4718)

Question 1153115: 4) A group of 1455 students were surveyed about the courses they were taking at their college with the results organized in the following Venn diagram:
There are four circles
Math: I. 44 II.59 V.137 VII.80 VI.151 IX.163 IV.43
Science: II.59 III.149 V.137 VI.151 VII.80 VIII.160 X. 80
Dance: VIII.160 VII.80 V.137 IV.43 VI.151 IX.163 X.88
English: VI.151 VII. 80 VIII.160 X.88 IX.163 XII.34
outside of the diagrams: XIV.66
A student is drawn at random from the group of surveyed students. Find each of the following, rounding your answer to 4 decimal places.
a) What is the probability that the student is taking none of the courses?
Round your answer to 4 decimal places.

b) What is the probability that the student is not taking Science?
Round your answer to 4 decimal places.

c) What is the probability that the student is taking Math & English or are taking Science & Dance?
Round your answer to 4 decimal places.

d) What is the probability that the student is taking Math, Science, and English, but not Dance?
Round your answer to 4 decimal places.

e) What is the probability that the student is taking Science, but not Dance?
Round your answer to 4 decimal places.

f) What is the probability that the student is not taking Dance & English or is taking Dance & Math?
Round your answer to 4 decimal places.

g) What is the probability that the student is not taking Science, Dance, or English?
Round your answer to 4 decimal places.

h) What is the probability that the student is taking Math given they are taking English
Round your answer to 4 decimal places.

i) What is the probability that the student is taking Math, Science, or English?
Round your answer to 4 decimal places.

i) What is the probability that the student is taking Math and English, but not Dance?
Round your answer to 4 decimal places.

Click here to see answer by ikleyn(52750)

Question 1153186: suppose that the average length of life of color television tube is 12 months what is the probability that the length of life is equal to greater than 18 months
Click here to see answer by Theo(13342)

Question 1153088: The graph illustrates the distribution of test scores taken by College Algebra students. The maximum possible score on the test was 140, while the mean score was 78 and the standard deviation was 15.
33 - 48 - 63 - 78 in the middle - 93 - 108 - 123
Distribution of Test Scores

What is the approximate percentage students who scored between 63 and 93 on the test?
%
What is the approximate percentage of students who scored between 48 and 108 on the test?
%
What is the approximate percentage of students who scored between 78 and 123 on the test?
%
What is the approximate percentage of students who scored higher than 123 on the test?
%

I would like to know how to solve, thank you
Click here to see answer by Theo(13342)

Question 1153188: .
Consider a t distribution with
22
degrees of freedom. Compute
P
≤
t
−
1.31
.
Click here to see answer by ikleyn(52750)

Question 1153190: A manufacturer claims that the mean lifetime,
μ
, of its light bulbs is
45
months. The standard deviation of these lifetimes is
4
months. Ninety bulbs are selected at random, and their mean lifetime is found to be
44
months. Can we conclude, at the
0.05
level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from
45
months?
Perform a two-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table.
The null hypothesis:
H
0
:

The alternative hypothesis:
H
1
:

The type of test statistic:

The value of the test statistic:
(Round to at least three decimal places.)

The two critical values at the
0.05
level of significance:
(Round to at least three decimal places.)
and
Can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from 45 months?
Click here to see answer by ikleyn(52750)

Question 1153184: Double O’s café serves two desserts, cake, and pie. They also serve three beverages, coffee, tea, or juice. Suppose you choose one dessert and one beverage. How many possible outcomes are there?
Click here to see answer by ikleyn(52750)

Question 1153204: At a small midwestern college, a survey determined that 61% of freshmen participated in intercollegiate athletics. Further 48% participated in a campus social club. However, 18% did not participate in either type of activity. What percentage participated in either sports or a social club?
Click here to see answer by ikleyn(52750)

Question 1153206: At a small midwestern college, a survey determined that 61% of freshmen participated in intercollegiate athletics. Further 48% participated in a campus social club. However, 18% did not participate in either type of activity. What percentage participated in either sports or a social club? From the same survey, what percentage of freshman participated in both sports and a social club?
Click here to see answer by ikleyn(52750)

Question 1153244: suppose q loaves of bread cost c rand. indicate an expression for the cost in rand of 3 loaves for bread
Click here to see answer by josgarithmetic(39613)

Question 1153244: suppose q loaves of bread cost c rand. indicate an expression for the cost in rand of 3 loaves for bread
Click here to see answer by MathTherapy(10549)

Question 1153298: Suppose that a family has 4 children. Also, suppose that the probability of having a girl is one half
. Find the probability that the family has the following children.
Exactly 3 girls and 1 boy
Click here to see answer by MathLover1(20849)

Question 1153209: An IRS auditor randomly selects 3 tax returns from 61 tax returns of which 9 contain errors. What is the probability that she selects all those containing errors? This is unusual probability?
Click here to see answer by math_helper(2461)

Question 1153300: Not all visitors to a certain company's website are customers. In fact, the website administrator estimates that about of all visitors to the website are looking for other websites. Assuming that this estimate is correct, find the probability that, in a random sample of visitors to the website, exactly actually are looking for the website.
Click here to see answer by ikleyn(52750)

Question 1153304: Thirty five percent of consumers prefer to purchase electronics online. You randomly select 8 consumers. Find the probability that the number of consumers who prefer to purchase electronics online is (a) exactly five, (b) more than five, and (c) at most five.
(a) Find the probability that the number that prefer to purchase electronics online is exactly five

Click here to see answer by Boreal(15235)

Question 1153276: In a random sample of six mobile devices, the mean repair cost was $60.00 and the standard deviation was $11.00. Assume the population is normally distributed and use at-distribution to find the margin of error and construct a 99% confidence interval for the population mean. Interpret the results.
The 99% confidence interval for the population mean mu is ( ), ( )
(Round to two decimal places as needed.)
The margin of error is ( _ )(Round to two decimal places asneeded.)
Click here to see answer by Boreal(15235)

Question 1153250: A baseball player has a batting average of 0.15. What is the probability that he has exactly 1 hits in his next 7 at bats?
The probability is??

Click here to see answer by Boreal(15235)

Question 1153189: The mean height of a certain kind of plant is
157
centimeters. Suppose we want to carry out a hypothesis test to see if the mean height when these plants are treated with a certain chemical differs from
157
. State the null hypothesis
H
0
and the alternative hypothesis

Click here to see answer by Boreal(15235)

Question 1153031: In a study, 31% of adults questioned. Among 13 randomly selected, only 1 reported that their health was excellent.
a) Find the Probability that when 13 adults are randomly selected, exactly 1 is in excellent health.
b) Find the probability that when 13 adults are randomly selected, at most 1 is in excellent health.
I'm having trouble on trying to figure out what formula to use for these questions.. and how to remember which ones to use for questions like these.
Thank you.
Click here to see answer by Boreal(15235)

Question 1153347: Determine whether these events are mutually exclusive.
a. Roll a die: Get an even number and get a number
less than 3.
b.Roll a die: Get a prime number (2, 3, 5) and get an
odd number.
c. Roll a die: Get a number greater than 3 and get a
number less than 3.
d. Select a student in your class: The student has blond
hair and the student has blue eyes.
Click here to see answer by Boreal(15235)

Question 1153179: A researcher believes that smoking affects a person’s sense of smell. To test this, he takes a sample of 25 smokers and gives them a test of olfactory sensitivity. In this test, higher scores indicate greater sensitivity. For his sample, the mean score on the test is 14.8 with a standard deviation of 2.4. The researcher knows the mean score in the population is 16.2, but the population standard deviation is unknown.
(a) What are the null and alternative hypotheses in this study (stated mathematically)?
(b) Should the researcher use a one-tailed or a two-tailed test?
(c) Compute the appropriate test statistic for testing the hypothesis.
(d) Using α = 0.01, do you conclude that smoking affects a person’s sense of smell? Be sure to include a discussion of the critical value in your answer.
(e) What type of error might the researcher be making in part (d)?
Click here to see answer by Boreal(15235)

Question 1152707: Consider a random experiment of tossing a coin three times (a) Find the sample space 𝑺𝑺𝟏𝟏 if we ish to observe the exact sequences of heads and tails obtained (b) Find the sample space 𝑺𝑺𝟐𝟐 if we wish to observe the number of heads in the three tosses.
Click here to see answer by Boreal(15235)

Question 1152710: The mean amount purchased by each customer at Churchill’s Grocery Store is $35 with a standard deviation of $9. The population is positively skewed. For a sample of 42 customers, answer the following questions:

a. What is the likelihood the sample mean is at least $39? (Round the z-value to 2 decimal places and the final answer to 4 decimal places.)

Sample mean

b. What is the likelihood the sample mean is greater than $33 but less than $39? (Round the z-value to 2 decimal places and the final answer to 4 decimal places.)

Sample mean

c. Within what limits will 98% of the sample means occur? (Round the final answers to 2 decimal places.)

Sample mean
Click here to see answer by Boreal(15235)

Question 1153359: A research firm conducted a survey to determine the mean amount Americans spend on coffee during a week.
They found the distribution of weekly spending followed the normal distribution with a population standard deviation of $5.
A sample of 49 Americans revealed that Xbar=$20.

What is the point estimate of the population mean?
Using the 95% level of confidence, determine the confidence interval for μ.
Click here to see answer by jim_thompson5910(35256)

Question 1153363: How to interpret the answere of .46
Click here to see answer by ikleyn(52750)

Question 1153346: A school dance committee is made up of 3 freshmen, 6 sophomores, 3 juniors, and 2 seniors.
How many ways are there to sit the committee in a row at a meeting if the students must sit together by grade?
How many ways are there to sit the committee in a row at a meeting if the freshman, sophomores, and juniors must sit by grade, but the seniors can sit wherever they want?
Click here to see answer by jim_thompson5910(35256)

Question 1153366: A coin is weighted so that there is a 58% chance that it will come up "heads" when flipped.
The coin is flipped four times. Find the probability that all four flips resulted in "heads".
Click here to see answer by ikleyn(52750)

Question 1153372: A coin is weighted so that there is a 75% chance that it will come up "heads" when flipped.
The coin is flipped four times. Find the probability that the first three flips resulted in "heads", and the last flip resulted in "tails".
Click here to see answer by Alan3354(69443)

Question 1153379: If two dies are rolled one time, find the probability of getting these results
1. A sum less than 9
2. A sum greater than 9
Click here to see answer by Edwin McCravy(20054)

Question 1153419: A coin is weighted so that there is a 62% chance that it will come up "heads" when flipped.
The coin is flipped four times. Find the probability of getting two "heads" and two "tails".
Click here to see answer by ikleyn(52750)

Question 1153418: A coin is weighted so that there is a 59% chance that it will come up "heads" when flipped.
The coin is flipped four times. Find the probability of getting exactly three heads.
Round your
Click here to see answer by ikleyn(52750)

Question 1153453: In a proposed business venture, a businesswoman estimates there is a 70% chance she will make $59000 and a 30% chance she will lose $55000. Determine her expected value
Click here to see answer by ikleyn(52750)

Question 1153452: 3 hunters have probabilities 2/5, 1,2 and 3/4 of hiting a target. Find the Probability that:
(a) All hits the Target
(b) Hits the Target
(c). None hits the Target
(c) One hits the Target
Click here to see answer by ikleyn(52750)

Question 1153473: A business graduate wants to get a job in any one of the top 10 accounting firms. Applying to any of these companies requires a lot of effort and paperwork and is therefore costly. She estimates the cost of applying to each of the 10 companies and the probability of getting a job offer there. These data are tabulated below. The tabulation is in the decreasing order of cost
Company 1 2 3 4 5 6 7 8 9 10
Cost (S) 870 600 540 500 400 320 300 230 200 170
Probability 0.38 0.35 0.28 0.20 0.18 0.18 0.17 0.14 0.14 0.08
a) If the graduate applies to all 10 companies, what is the probability that she will get
atleast one offer?
b) If she applies to companies 2. 5. 8. and 9, what is the total cost?

Click here to see answer by ikleyn(52750)

Question 1153484: For a continuous random variable X, P(20 ≤ X ≤ 66) = 0.31 and P(X > 66) = 0.25. Calculate the following probabilities. (Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 2 decimal places.)
a. P(X < 66)
b. P(X < 20)
c. P(X = 66)

Click here to see answer by greenestamps(13195)

Question 1153490: There are 16 students giving final presentations in your history course.
(a) Three students present per day. How many presentation orders are possible for the first day?
(b) Presentation subjects are based on the units of the course. Unit B is covered by three students, Unit C is covered by five students, and Units A and D are each covered by four students. How many presentation orders are possible when presentations on the same unit are indistinguishable form each other?
Click here to see answer by ikleyn(52750)

Question 1153512: Almost all medical schools require applicants to take the Medical College Admission Test (MCAT). To estimate the mean score of those who took the MCAT at WSSU, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 6.5. Suppose that (unknown to you) the mean score of those taking the MCAT at WSSU is 25.0. If you sample 25 students, what is mean of the sampling distribution of x-bar?
Click here to see answer by Boreal(15235)

Question 1153531: About 3% of children in a country are allergic to peanuts. Choose three children at random and let the random variable X be the number in this sample who are allergic to peanuts. The possible values X can take are 0, 1, 2, and 3. What is the conditional probability that exactly two of the children will be allergic to peanuts, given that at least one of the three children suffers from this allergy? (Round your answer to four decimal places.)
Click here to see answer by Boreal(15235)

Question 1153536: A box contains 9 green marbles, 9 blue marbles, and 5 red marbles.
Three marbles are selected at random from the box, one at a time, without replacement.
Find the probability that the three marbles selected are all different colors.
Click here to see answer by VFBundy(438)

Question 1153535: A box contains 7 green marbles, 8 blue marbles, and 4 red marbles.
Three marbles are selected at random from the box, one at a time, without replacement.
Find the probability that the first marble is red, the second marble is green, and the third marble is blue.
Click here to see answer by VFBundy(438)

Question 1153534: In a large statistics course, 72% of the students passed the first exam, 70% of the students pass the second exam, and 59% of the students passed both exams.
Assume a randomly selected student is selected from the class. If the student passed the first exam, what is the probability that they passed the second exam?
Click here to see answer by VFBundy(438)

Question 1153533: Use the information below to calculate P(A|B).
P(A) = 0.529
P(B) = 0.46
P(A or B) = 0.703
Click here to see answer by jim_thompson5910(35256)

Question 1153493: A security code consists of a person's first and last initials and four digits. Use 8 decimals places.
(a) What is the probability of guessing a person's code on the first try?
(b) What is the probability of not guessing a person's code on the first try?
(c) You know a person's first name and that the last digit is odd. What is the probability of guessing this persons code?
(d) Are the statements in parts (a) - (c) examples of classical probability, empirical probability, or subjective probability?
Click here to see answer by Boreal(15235)

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