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

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

Question 1175807: The distribution of scores on a recent quiz in Mr. Waldron's statistics class is approximately normal. About 2.5% of the students scored below 25 on the quiz. 84% of the students scored below 40 on the quiz. Use the 68-95-99.7 rule to estimate the mean and standard deviation of the quiz scores in this class. Make sure to show your work and justify your answer.
Click here to see answer by Boreal(15235)

Question 1175798: A local university offers a review course for those who are planning to take
the CPA exam. 30% of the people who took the exam had attended the
university’s CPA review course. The results of the test showed that 60% of
those who attended the CPA review course passed the exam. Among those
who did not attend the course, only 20% passed the exam.
If an individual passes the exam, what is the probability that he attended the
CPA review course?
Can someone help me with the equation to find this answer, please?
Click here to see answer by ewatrrr(24785)

Question 1175796: 37% of the squirrels in Cititon Park are gray. What is the probability that, in a random sample of 174 squirrels, less than 64 are gray squirrels? Use a normal approximation to compute your answer. Round your answer to 4 decimal places.
Click here to see answer by Boreal(15235)

Question 1175782: Ali is a student taking statistics course unfortunately Ali is not a good student Ali does not read the book before class and does not do homework and misses classes. Ali intend to rely on quiz. Quiz consist of 10 multiple choice questions.each have 5 possible answer and only one is correct.
(a) What is the probability that Ali gets no correct answer?
(b) What is the probability that Ali gets 2 correct answe?
(c) What is the probability that Ali gets all correct answer?
(d) What is the probability that Ali gets 2 to 5 correct answer?
Click here to see answer by Boreal(15235)

Question 1175769: The average number of days school is closed due to snow during the winter in a certain city in the eastern part of united states is 4. What is the probability that the schools in this city will close for less than 3 days during a winter?
Click here to see answer by Boreal(15235)

Question 1175783: The ice cream shop has 7 types of toppings available, and you decide to add 3 toppings to your bowl of 3 scoops of ice cream. How many combinations of 3 scoops of ice cream and 3 toppings are possible?
Click here to see answer by greenestamps(13195)

Question 1175773: Ali is a student taking a statistics course. Unfortunately, Ali is not a good student. Ali does not read the textbook before class, does not do homework, and regularly misses classes. Ali intends to rely on luck to pass the next quiz, the quiz consists of 10 multiple choice questions. Each question has five possible answers, only one of which is correct.
Ali plans to guess the answer to each question.
(a) What is the probability that Ali gets no answer correct?
(b) What is the probability that Ali gets two answer correct?
(c) What is the probability that Ali gets all answer correct?
(d) What is the probability that Ali gets 2 to 5 answer correct?
Click here to see answer by ikleyn(52750)

Question 1175747: Assume the random variable x is normally distributed with mean = 86 and standard deviation = 4. Find the indicated probility p(x<80
Click here to see answer by amarjeeth123(569)

Question 1175832: A company that manufactures shoes has three factories. Factory 1 produces 25% of the
company's shoes, Factory 2 produces 60%, and Factory 3 produces 15%. One percent of the
shoes produced by Factory 1 are mislabeled, 0.5% of those produced by Factory 2 are
mislabeled, and 2% of those produced by Factory 3 are mislabeled. If you purchase one pair of
shoes manufactured by this company, what is the probability that the shoes are mislabeled?
Click here to see answer by ikleyn(52750)

Question 1175835: Two men nd three women are in a committee. Two of the
five are to be chosen to serve as officers. What is the probability that one of the two selected persons is a man and the other is a woman?
Click here to see answer by ikleyn(52750)

Question 1175745: You are dealt one card from a standard 52-card deck. What is the probability, as a reduced fraction, of being dealt a card greater than 3 but less than 7?
Click here to see answer by CubeyThePenguin(3113)

Question 1175856: Solve completely. Follow the procedure below:
A. Setup the null and alternate hypothesis
B. What is the level of significance “a” (alpha)? What test will you use and how many tails is it?
C. Find the Critical Value given the level of significance and the number of tails (and the given n if it is a t-test). Draw a
bell curve.
D. Write the Decision Rule given the Critical Value. Note: A two-tailed test will have a positive and a negative Critical Value.
E. Solve for the test statistic (z or t-test). Compare with the Critical Value.
F. Conclusion: Reject or Do Not Reject? Explain in terms of the decision rule.
z-test

3. A cheerleading squad received a mean rating (out of 100 possible points) of 75 with a standard deviation of 7 in competitions over the previous three seasons. The same cheerleading squad performed in 36 local competitions this season with a mean rating equal to 78 in competitions. Determine whether mean ratings increased this season (compared to the previous three seasons) at a .04 level of significance.
Click here to see answer by ewatrrr(24785)

Question 1175855: Solve completely. Follow the procedure below:
A. Setup the null and alternate hypothesis
B. What is the level of significance “a” (alpha)? What test will you use and how many tails is it?
C. Find the Critical Value given the level of significance and the number of tails (and the given n if it is a t-test). Draw a
bell curve.
D. Write the Decision Rule given the Critical Value. Note: A two-tailed test will have a positive and a negative Critical Value.
E. Solve for the test statistic (z or t-test). Compare with the Critical Value.
F. Conclusion: Reject or Do Not Reject? Explain in terms of the decision rule.
z-test

4. The police force has a mean physical fitness rating of 72 points (on a 100-point physical endurance rating scale) and a standard deviation of 9 points. The police chief selects a sample of 64 police officers. They score a mean physical fitness rating of 74. Did the physical endurance of the police force change at a .05 level of significance?

Click here to see answer by ewatrrr(24785)

Question 1175858: You are dealt one card from a standard 52-card deck. What is the probability, as a reduced fraction, of being dealt a face card?
Click here to see answer by CubeyThePenguin(3113)

Question 1175768: Create a sample of size 5 whose mean is 10 and whose variance is zero?
Click here to see answer by CubeyThePenguin(3113)

Question 1175829: A jury consists of five men and seven women. Four are selected at random for an interview.
a) Find the probability that all four selected people are men.
b) Find the probability that two men and two women are selected.
Click here to see answer by ewatrrr(24785)

Question 1175861: Is this correct? I want to check my answer.
Lewis is saving for a down payment of $8,750 on a house. The initial amount of money he has saved is $250, and the amount of money he plans on saving every month is $340. To model the situation, he created this equation, where x represents the number of months and y represents the total amount of savings:
y = 250 + 340x.
Determine the missing steps and justifications.

The question and table is provided in the link here: https://i.imgur.com/Jeq3QUR.png
Click here to see answer by CubeyThePenguin(3113)

Question 1175831: Please help me out with this questions. I appreciate thanks.
Based on the data shown below, calculate the correlation coefficient (to three decimal places)
x y
4 16.83
5 12.44
6 14.15
7 9.66
8 8.87
9 8.18
10 5.99
11 4.1
Write an equation in the form y=mx+by=mx+b for the following table:
x y
-4 -28
-2 -12
0 4
2 20
4 36
6 52
8 68
10 84

y=

Click here to see answer by ewatrrr(24785)

Question 1175854: Solve completely. Follow the procedure below:
A. Setup the null and alternate hypothesis
B. What is the level of significance “a” (alpha)? What test will you use and how many tails is it?
C. Find the Critical Value given the level of significance and the number of tails (and the given n if it is a t-test). Draw a
bell curve.
D. Write the Decision Rule given the Critical Value. Note: A two-tailed test will have a positive and a negative Critical Value.
E. Solve for the test statistic (z or t-test). Compare with the Critical Value.
F. Conclusion: Reject or Do Not Reject? Explain in terms of the decision rule.
z-test

1. A generic brand of the anti-histamine Diphenhydramine markets a capsule with a 50 milligram dose. The manufacturer is worried that the machine that fills the capsules has come out of calibration and is no longer creating capsules with the appropriate dosage. To test this at 0.05 level of significance, a random sample study was done for 36 capsules that yielded an average of 47 mg. with sample standard deviation of 8 mg. Does the data suggest that the population mean dosage of this brand is less than 50 mg?

Click here to see answer by ewatrrr(24785)

Question 1175867: Are these correct? I want to check my answers.
Lewis is saving for a down payment of $8,750 on a house. The initial amount of money he has saved is $250, and the amount of money he plans on saving every month is $340. To model the situation, he created this equation, where x represents the number of months and y represents the total amount of savings:
y = 250 + 340x.
Determine the missing steps and justifications.
The question and table is provided in the link here: https://i.imgur.com/Jeq3QUR.png
Click here to see answer by Theo(13342)

Question 1175869: In a town, 53% of the residents voted for Candidate F. If we randomly survey 4 residents, what is the probability that at least one of them did not vote for Candidate F?
Click here to see answer by ewatrrr(24785)

Question 1175749: Use the appropriate formula to find the mean,The madian,and the mode of each grouped data.
scores: Frequency:
175-179. 1
170-174. 6
165-169. 8
160-164. 10
155-159. 22
150-154. 15
145-149. 16
140-144. 2
Click here to see answer by CubeyThePenguin(3113)

Question 1175952: Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution.
n = 12, = 23.6, s = 6.6, 99% confidence
A. 17.68 < μ < 29.52
B. 17.56 < μ < 29.64
C.18.42 < μ < 28.78
D.17.70 < μ < 29.50

Click here to see answer by Boreal(15235)

Question 1175884: A study found that 61% of green turtles migrate to warmer climates when seasons change. Scientists tagged 120 green turtles before migration. What is the probability that less than 20 green turtles did not migrate to a warmer climate during the season change?

Mean:

Variance:

Standard Deviation:
Click here to see answer by Boreal(15235)

Question 1175970: 1. The probabilities that a shop will make a profit and break even are 0.6 and 0.1 respectively. What is the probability that the shop will lose
Click here to see answer by Solver92311(821)

Question 1175971: 4. 6 men and 4 women applied for a temporary job. If 2 applicants from this group are randomly selected for an interview, find the probability that there is at least 1 woman.
Click here to see answer by ikleyn(52750)

Question 1175976: Consider the relation D = 0.023×a1^0.8 ×a2^0.3 where a1 and a2 are measured quantities. If a1 = 20000±125 and a2 = 5.5±0.2, determine the uncertainty for the parameter D.
Click here to see answer by ikleyn(52750)

Question 1175894: A Statistical survey shows that 28% of all men take size 9 shoes what is the Statistical survey shows that 28% of all men take size 9 shoes
Click here to see answer by ewatrrr(24785)

Question 1175386: The American Automobile Association reports that the
average time it takes to respond to an emergency call is
28 minutes. Assume the variable is approximately
normally distributed and the standard deviation is 9.002
minutes. If 70 calls are randomly selected, approximately
how many will be responded to in less than 15 minutes? How many will be responded to in 50 percent ? hwo many will be 100 percent?
Click here to see answer by Boreal(15235)

Question 1175474: 1. Test the claim that the proportion of people who own cats is smaller than 90% at the 0.01 significance level. The null and alternative hypothesis would be:
H0:p≥0.9
H1:p<0.9
Based on a sample of 500 people, 83% owned cats
What is The test statistic is: (2 decimal places)
The p value (2 decimal places).
2. You wish to test the following claim ( Ha ) at a significance level of α= 0.001.
Ho:p=0.61
Ha:p>0.61

You obtain a sample of size n= 382 in which there are 240 successful observations. For this test, you should use the (cumulative) binomial distribution to obtain an exact p-value. (Do not use the normal distribution as an approximation for the binomial distribution.) The p-value for this test is (assuming Ho is true) the probability of observing...
Click here to see answer by Boreal(15235)

Question 1174838: A smartphone company is interested in comparing the quality of work at two of its factories. By randomly selecting samples of smartphones manufactured at each factory and testing their reliability, the company will be able to estimate the proportion of malfunctioning smartphones manufactured at each factory. Of particular interest is the difference between these proportions. Independent simple random samples from the two offices provide the following information:
Factory 1
Factory 2
n1 = 250
n2 = 300
Number of malfunctioning phones = 35
Number of malfunctioning phones = 27

a. What is the point estimate of the difference between the two population proportions (p1 - p2)? 2pts
b. Develop a 95% confidence interval for the difference between the two population proportions (p1 - p2). 7pts
c. Develop a 90% confidence interval for the difference between the two population proportions (p1 - p2). 7pts
Click here to see answer by Boreal(15235)

Question 1176007: A sample of 110 adults has a mean body temperature of 98.18.
a. Assuming that the population of healthy adults has a mean body temperature of mu = 98.6 with a standard deviation of sigma = 0.58, approximate the probability that a sample of 110 has a mean less than 98.18. (P(xBar sub 110) <= 98.18)
b. What if anything do the results say about the belief that the average body temperature is 98.6?
Click here to see answer by ewatrrr(24785)

Question 1176008: A certain college has 52 students participating in games.30 play netball, 25 play football , 10 play handball and football ,13 play netball and handball,9 play netball and football while 2 play all the three games. How many students play handball and no other game?
Click here to see answer by ewatrrr(24785)

Question 1176015: Two men and three women are in a committee. Two of the
five are to be chosen to serve as officers. What is the probability that one of the two selected persons is a man and the other is a woman? Assume no replacement.
Click here to see answer by ikleyn(52750)

Question 1176014: The distribution of the number made by a class of student last month:
Number of donations made: 1 2 3 4 5
Number of students: 20 5 2 4 2
If a student is elected at random, find the probabilities of the following.
A. the student did not make any donations last month
B. The student made 1 or 2 donation last month
C. The student made more than 3 donations last month
Click here to see answer by ewatrrr(24785)

Question 1176034: In rolling a die , find the probability of getting an even number or a number that is a multiple of 3?
Click here to see answer by Edwin McCravy(20054)

Question 1176043: what is the probability as a decimal to the nearest hundredth that a person was not born on a month that begins with the letter?
Click here to see answer by ikleyn(52750)

Question 1176021: The Smith family was one of the first to come to the U.S. They had 9 children. Assuming that the probability of a child being a girl is .5, find the probability that the Smith family had:
at least 6 girls?

at most 4 girls?
Click here to see answer by ikleyn(52750)

Question 1176022: A psychologist is interested in constructing a 95% confidence interval for the proportion of people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain. 61 of the 813 randomly selected people who were surveyed agreed with this theory.
a. With 95% confidence the proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain is between___
and____
.
b.If many groups of 813 randomly selected people are surveyed, then a different confidence interval would be produced from each group. About___ percent of these confidence intervals will contain the true population proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain and about___ percent will not contain the true population proportion.
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