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

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

Question 463118: Two six sided dice, with sides numbered 1 through 6 are rolled. If the dice are rolled 9000 times, about how many times would you expect the dice to have a sum of 8?
Click here to see answer by amoresroy(361)

Question 463145: A researcher predicts that level of marital satisfaction experienced by persons with children and persons without children differs. In order to test this hypothesis, the marital satisfaction of 242 randomly selected married persons is measured; 122 have no children (mean satisfaction = 7.42, s = 3.92) and 120 have one child (mean satisfaction = 6.72, s = 4.04). High scores indicate high satisfaction. If alpha is set at .05, the critical value of the test statistic is
Click here to see answer by edjones(8007)

Question 463178: 17% of published criminals are caught. If 200 are published, find the probability that between 25 and 40 inclusive are arrested.
I have tried finding the probability of 40 or less and subtracting it from 25 or less and that is incorrect. And I have tried finding probability of 40 or more and subtracting it from 25 or more. Any tips?
Click here to see answer by edjones(8007)

Question 463143: you work for a small corporation which has 3 field representatives A,B,C who telephone the home office for various reasons. Field rep A makes 45 percent of the calls, and rep B and C make 40 snd 15 percent of the calls, respectively. if A calls, then there is a 4 percent chance that she will ask for the VP in charge of sales for help in closing a deal, whereas if B or C, then there is a 10 percent or 22 percent chance of their asking for assistance. One of the field representatives calls and asks for the VP's help. Because you were on your lunch break , you didnt bother to write down the field reps name and you now cant remember who called. assuming you must relay the request whom should you say called?Explain carefully and completely, providing numerical evidence.

Click here to see answer by edjones(8007)

Question 463198: when a single card is drawn from an ordinary 52-card deck, find the odds in favor of getting a red 6 or a black 2
Click here to see answer by edjones(8007)

Question 463199: So I am really stumped on this problem. I am having a hard time drawing it on here for the tutors but any help would be greatly appreciated. You must start at A, which is in the left hand corner, and end at c which is in the right hand corner. B is located one row down from A and three rows across. The question asks how many different routes start at A, pass through B, and end at C if you can only move down or to the right when starting at A and ending at point C.
The graph has 5 rows and 5 columns.
It looks similar to this.
a
[][][]b[][]
[][][][][]
[][][][][]
[][][][][]
[][][][][]c
I first guessed the answer to be 3!5!2! but that was incorrect. Next I tried c(4,1)c(5,3)/c(10,5). Please show me how to set this up and solve it.
Click here to see answer by Edwin McCravy(20054)

Question 463299: Please help,
a wisconsin vet recorded the lifespan of cats shed cared for as follows:
18 9 13 12 13 10
what is the median lifespan in this example? explain your answer showing step-by-step calculatin.
Click here to see answer by edjones(8007)

Question 463294: In a sample bag of M&M's candy, there are 5 brown, 6 yellow, 4 blue, 3 green, and 2 orange. What is the probability of getting 1 brown and 2 orange M&M's if 3 are taken at a time? Show your work.
Click here to see answer by edjones(8007)

Question 463276: Historical data show that 4% of the components produced by a certain manufacturer are defective.Someone challenged the figure of 4% and the management wanted to test whether this claim has to be modified. If a random sample of 500 items resulted in 16 defective ones, is this significant evidence that the claim is incorrect?
By considering a significance level alpha = 0.05, what is the lowest rate of defective components that the manufacturer can claim, with the same experimental test results?

Click here to see answer by edjones(8007)

Question 463255: shirley is the best free throw shooter for fchs. she hits her free throws 81% of the time. find probability in a game, she makes her first free throw on her a) third try? b) on her 2nd or 4th try?
Click here to see answer by edjones(8007)

Question 463257: a sc tourist bureau survey showed that 85% of those who seek information about the state actually come to visit. the office received 8 requests for information. find: a) the probability that less than five of the people will visit sc?
b) the probability that at least 3 of thepeople will not visit sc?
c)probability that 2 to 6, inclusive, of the people will visit sc?
d)whats the expected number of visitors from this situation?

Click here to see answer by edjones(8007)

Question 463333: Suppose you roll a number cube 30 times. Wite a fraction to describe the theoretical probability of rolling 1
Click here to see answer by Alan3354(69443)

Question 463340: The owner of a bottling company is considering buying a new bottling machine. He has been testing two different machines that are being considered. After collecting 300 samples from each machine over several weeks, he was able to conduct a two sample z test.

He decided to utilize a 0.05 significant level for the test. The test was to address the claim that the mean weight of the bottles filled by the Orno machine was greater than the mean weight of the bottles filled by the Edne machine. The test statistics was 2.21. What is the decision regarding the hypothesis?
A. Reject the null hypothesis; there is a significant difference.
B. This is a two tail test and the critical value for the test is 1.96.
C. There is not enough data available to answer the question.
D. Accept the null hypothesis; there is not a significant difference

Click here to see answer by edjones(8007)

Question 463352: Supposing we perform the experiment of throwing a set of 3 dice coloured red,blue,and green.you are expected to obtain a probability distribution on the possible outcomes of this experiment.Determine the probability distribution of this experiment.
Click here to see answer by robertb(5830)

Question 463368: A test consists of 90 multiple choice questions, each with five possible answers, only one of which is correct. Find the mean and the standard deviation of the number of correct answers.
Click here to see answer by robertb(5830)

Question 463599: The male to female ratio is 5 to 4. There are 6975 students total. How many are female and how many are males?
Click here to see answer by checkley79(3341)

Question 463591: A teacher gives a quiz consisting of 4 questions each questions has 5 possible answers what is the probability of a student getting a 100% on the quiz if the student guesses at each?
Click here to see answer by checkley79(3341)

Question 463630: Two cards are drawn at random in succession, with replacement, from a standard deck of 52. Find the probability that both cards are kings.
Click here to see answer by edjones(8007)

Question 463606: Assume n> 30 is known and the population distribution is normal. Determine the critical z values for each of the following types of hypothesis tests:
a) right tailed test, a=.01
B) two tailed test a=.05
c) left tailed test a=.05
Click here to see answer by edjones(8007)

Question 463605: From a group of 18 customers,6 are to be chosen to receive a special gift. Assuming that the order in which the customers are chosen is irrelevant, how many groups of 6 customers can be chosen?

Click here to see answer by edjones(8007)

Question 463631: What is the probability of 6 of 22 homes being burglarized,when 24% of homes are burglarized?
Click here to see answer by edjones(8007)

Question 463609: In a random survey of 10 women in this age group, what is the probability that two or fewer were never married?

Click here to see answer by edjones(8007)

Question 463592: Find the indicated probability.

A bin contains 77 light bulbs of which 12 are defective. If 5 light bulbs are randomly selected from the bin with replacement, find the probability that all the bulbs selected are good ones.

Click here to see answer by edjones(8007)

Question 463575: . A Las Vegas casino surveyed 180 gamblers. The results are as follows:
62 played poker
91 played blackjack
28 played both
Construct a Venn diagram and submit it to the Drop box.
Answer the following questions:
i. How many played only blackjack?
ii. How many played only poker?
iii. How many played either one or the other or both?
iv. How many played neither?

Click here to see answer by edjones(8007)

Question 463651: A person scores 81 on a test of verbal ability and 6.4 on a test of quantitative
ability. For the verbal ability test, the mean for people in general is 50 and the
standard deviation is 20. For the quantitative ability test, the mean for people in
general is 0 and the standard deviation is 5. Which is this person�s stronger ability:
verbal or quantitative? Explain your answer to a person who has never had a
course in statistics.
Click here to see answer by edjones(8007)

Question 463662: In San Francisco, a sample of 3,298 wireless routers showed that 35.03 percent used encryption(to prevent hackers from intercepting information). In Seattle, a sample of 3,193 wireless routers showed that 33.62 percent used encryption.

Click here to see answer by edjones(8007)

Question 463657: I have posted this problem a couple of times, but havent gotten a reply. this is what I have done so far. Does it look like im doing it right?
Time spent on the internet
given the bar graph below, create a grouped frequency distribution.
along the side of the graph are numbers from the bottom 0 to 9 at the top labeled hours per day.
along the bottom are the names barbara to 3, rosie to the 3, carlos 1, soon yi 6, scott 2, deborah 8, pat 4, cynthia 1.
ie, w=(l-s)/c
l-s=8-1=7
time spent from 8 deborah to 1 carlos and cynthia=class width.
class width=(largest data-smallest data)/number of classes
ie,w=(8-1)=7. divide into 4 classes, ie c=4
w=7/4=1.75
round 1.75 to 2.
Groups A,B,C,and D.
A:Cynthia,Carlos,Scott
B:Pat,Barbara,Rosie
C:Soon Yi
D:Deborah
And show them on a graph:
numbered up the side from the bottom 0-3.
listed in groups along the bottom 1-2,3-4,5-6,7-8
Please any input would be wonderful.
Click here to see answer by edjones(8007)

Question 463652: A person scores 81 on a test of verbal ability and 6.4 on a test of quantitative
ability. For the verbal ability test, the mean for people in general is 50 and the
standard deviation is 20. For the quantitative ability test, the mean for people in
general is 0 and the standard deviation is 5. Which is this person�s stronger ability:
verbal or quantitative? Explain your answer to a person who has never had a
course in statistics.
Click here to see answer by edjones(8007)

Question 463588: Can someone help me with this math problem, it is the last one i have to do to finish my homework.
given the graph below, create a grouped frequency distribution.
Time spent on the internet.
along the side are numbers from the bottom 0 to the top 9.
along the bottom are the names barbara that goes to number 3, rosie 3, carlos 1, soon yi 6, scott 2, deborah 8, pat 4, and cynthia 1.
please, please, help me.
Click here to see answer by edjones(8007)

Question 463675: The sales manager of a rental agency claims that the monthly maintenance fee for a condominium in the Lakewood region is $86. Past surveys showed that the standard deviation of the population is $6. A sample of 15 owners shows that they pay an average of $84. Test the manager�s claim at α = 0.01. Find the 99% confidence interval of the mean. Does the confidence interval interpretation agree with the results of the hypothesis test? Explain. Assume that the variable is normally distributed.
Click here to see answer by edjones(8007)

Question 463673: A ski shop manager claims that the average of the sales for her/his shop is $1800 a day during the winter months. Ten winter days are selected at random, and the mean of the sales is $1830. The standard deviation of the population is $200. Can one reject the claim at α = 0.05? Find the 95% confidence interval of the mean. Does the confidence interval interpretation agree with the hypothesis test results? Explain. Assume that the variable is normally distributed
Click here to see answer by edjones(8007)

Question 463672: Find the critical value (or values) for the t test for each.
a.n = 10, α = 0.05, right-tailed
b.n = 18, α = 0.10, two-tailed
c.n = 6, α = 0.01, left-tailed
d.n = 9, α = 0.025, right-tailed
e.n = 15, α = 0.05, two-tailed
Click here to see answer by edjones(8007)

Question 463713: A student takes a 20 question, multiple choice exam with 5 choices for each question. If the student is guessing, find the following probabilities:
A. Getting less than 5 questions right?
B. Passing the exam with at least an 80% score?
C. Getting every question but 2 wrong?
Please help?!?
Click here to see answer by reviewermath(1029)

Question 463771: Two cards are drawn at random in succession, with replacement, from a standard deck of 52. Find the probability that both cards are kings.
Click here to see answer by rfer(16322)

Question 463840: a small company finds the probability of a single phone being engaged is 0.8
the company wants to improve thier service to customers by providing sufficient phones so that the probability of a phone being engaged is less than 0.5.
how many phones do they need ?
HELPPPPP !!!!!!!!1

Click here to see answer by sudhanshu_kmr(1152)

Question 463862: A bookcase contains 2 statistics books and 4 biology books. If 2 books are chosen at random, the chance that both are statistics books is
Click here to see answer by sudhanshu_kmr(1152)

Question 463924: A bag contains a total of 15 batteries, of which five are defective. Selecting two at random, without replacement, determine the probability that none of the batteries you select are good.
Click here to see answer by sudhanshu_kmr(1152)

Question 463925: In how many different ways can the top ten new indie bands be ranked on a top ten list? The top hit song for each of the ten bands will compete to receive monetary awards of $1000, $500, $250 and $100, respectively. In how many ways can the awards be given out?
Click here to see answer by edjones(8007)

Question 463861: A bookcase contains 2 statistics books and 4 biology books. If 2 books are chosen at random, the chance that both are statistics books is
Click here to see answer by edjones(8007)

Question 463873: Assume I drew 2 random samples of University of Phoenix students, gave them a statistics exam, and one group (men) had a 76 average score and the other group (women) had an average score of 80. Is it possible that things are not as they seem -- that the women are smarter than the men? Note: the standard deviation of the men's scores was 8 and the women's scores was 6. There were 36 in each sample.
Click here to see answer by edjones(8007)

Question 464000: You roll two dice. What is the probability of getting a 3 or a 6 on the second die, given that you rolled a 1 on the first die?
Click here to see answer by edjones(8007)

Question 463999: You have 7 old books and need to choose 4 to give away. How many different groups of 4 books can you make?
Click here to see answer by edjones(8007)

Question 463996: Which of the choices is the variance of the sample shown here?
35, 36, 41, 56, 60, 71

Click here to see answer by edjones(8007)

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