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

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

Question 580870: If two people are randomly selected (with replacement) from a class containing 16 psychology students and 13 nursing students, what is the probability of selecting in order: 2 psychology students?
Click here to see answer by stanbon(75887)

Question 580998: Lynn's snack bag contains only red and green grapes. the number of green grapes is 5 more then the number of red grapes. if the probability of selecting green grapes is 10/15. how many red grapes are in the bag? How many green grapes?
Click here to see answer by dfrazzetto(283)

Question 581063: I need help explaining how to find the answer to what is 1/5 of 15 to my son.
Click here to see answer by ankor@dixie-net.com(22740)

Question 581083: A letter is chosen from the words BABY BOY and the replaced.
Find P(B and B).
Click here to see answer by stanbon(75887)

Question 581068: a bag of marbles has 313 red marbles and 110 blue ones. if i bought 4 bags of marbles how many red marbles did i buy?
Click here to see answer by stanbon(75887)

Question 581023: If the probability of having at least 1 boy in a 2-child family is 0.65, what is the probability of having 2 girls?
I was thinking that maybe i can multiply 1/ 0.65 x 2/1 but i dont think that's the solution.
Click here to see answer by stanbon(75887)

Question 580993: Hi there, please help:)
Consider a box which has 7 red balls and 4 green balls:
a. Find the probability of drawing a red ball on the first draw and a green ball on the second draw, if you do not return the first ball to the box.
b. Find the probability of drawing a green ball on the first draw and a green ball on the second draw, if you do return the first ball to the box.
Thanks,
Fiona
Click here to see answer by stanbon(75887)

Question 580990: if X is a binomial random variable with n=37 and p=.39, find
a. What is the expected value?
b. what is the standard deviation?
Click here to see answer by stanbon(75887)

Question 580977: Hi there, please help :)
consider finding the probabilty of getting 6 hearts out of 10 draws from a deck of cards if after each draw the card is returned to the deck.
A) Does this meet the conditions of a binomial experiment?
b) if so, what is the probability?

Click here to see answer by stanbon(75887)

Question 581108: A coin is tossed three times. Find the probability that the coin lands on tails, then heads,then tails.
Click here to see answer by stanbon(75887)

Question 580957: At one high school, the mean time for running the 100-yard dash is 15.2 seconds with a standard deviation of 0.9 seconds. The time are very closely approximated by a normal curve. Find the percent of times that are:
More than 15.2 seconds
Between 14.3 and 16.1 seconds
Thank you.
Click here to see answer by stanbon(75887)

Question 581007: a researcher is investigating the effectiveness of a new study-skills training program
Click here to see answer by richard1234(7193)

Question 581090: The scatter plot shows the average temperature each month in a particular city. What is a good prediction for the temperature in July if the temperature continues to increase until then?
Click here to see answer by richard1234(7193)

Question 581185: Mary purchased 9 plants, but only needed 6 plants to be planted. How many ways can she select the 6 plants to be planted?

Click here to see answer by stanbon(75887)

Question 581179: A machine produces bolts with a mean diameter of 0.30 inches and a standard deviation of 0.01 inches. The diameters are approximately normally distributed. What is the probability that a randomly selected bolt will have a diameter greater than 0.32 inches?
My answer = 0.023.
Thanks!!
Click here to see answer by stanbon(75887)

Question 581144: The probability of getting a red fruit candy from an assorted bag is 0.1.
There are 50 pieces of candy in a bag.
What is the probability that there are at least 4 pieces of red candy in the bag?
Click here to see answer by stanbon(75887)

Question 581130: The diameter of an electric cable is normally distributed, with a mean of 0.8 inch and a standard deviation of 0.01 inch. What is the probability that the diameter will exceed 0.82 inch?
Click here to see answer by stanbon(75887)

Question 580987: A research team at a university conducted a binomial study showing that approximately 10% of all businessmen who wear ties wear them so tight that they actually reduce blood flow to the brain, diminishing cerebral functions. At the board meeting of the 15 businessmen, all of whom wear ties, what is the probability that
a. exactly 6 ties are too tight?
b. at least one tie is too tight?
hint: P(at least one)=1-p(none)
c. at least 13 are not too tight?
Click here to see answer by stanbon(75887)

Question 580970: Hi there, PLease help :)
What would have to be the test score (rounded to once place to the right of a decimal) to qualify for admittance into a institution with a mean of normally distributed test scores of 82.5 and a standard deviation was 6.9, assuming admittance depended on being in the top 17 percent.
Thanks,
Fiona
Click here to see answer by stanbon(75887)

Question 581222: Please help I will pay for tutoring if I can get this answer right
The number of times the SAT was taken and the number of students are as follow
Number of times Number of students
1 721,769
2 601,325
3 166,736
4 22,299
5 6,730
Let x be a random variable indicating the number of times a student takes the SAT. Show the probability for this random vaiable.(to 4 decimals)
x=1
x=2
x=3
x=4
x=5
My answer was
1-7217.69
2-3006.62
Click here to see answer by stanbon(75887)

Question 581209: Scores on a test have a mean of 63 and Q3 is 82. The scores have a distribution that is approximately normal. Find the standard deviation. Round your answer to the nearest tenth.
Click here to see answer by stanbon(75887)

Question 580816: If the letters A, B, C, D, and E are to be used in a five-letter parking tag, how many different tags are possible if repetitions are not permitted?
Click here to see answer by stanbon(75887)

Question 581238: Fill in the P(X=x) values in the table below to give a legitimate probability distribution for the discrete random variable X, whose possible values are 0, 2, 4, 5, and 6. The table states that 0=0.29, 2=0.16, and 5=0.18. What are the values for 4 and 6?
Click here to see answer by stanbon(75887)

Question 581251: Let the random variable X follow a normal probability distribution with a mean 10 and a standard deviation of 2. Find P(X<15).
What I do know is it will not be 1 - # because of the sign, but I am not exactly sure where to start. Help!
Thank You
Click here to see answer by stanbon(75887)

Question 581254: Let the random variable X follow a normal probability distribution with a mean 10 and a standard deviation of 2.
Show your manual work of finding P(X>15).
What is known is it'll be 1 - # because the direction the sign goes, but other than that, I am not sure. Please help!
Thank You!
Click here to see answer by stanbon(75887)

Question 581206: For a standard normal distribution, find the percentage of data that are more than 2 standard deviations below the mean or more than 3 standard deviations above the mean.
Click here to see answer by stanbon(75887)

Question 581258: Let the random variable X follow a normal probability distribution with a mean 10 and a standard deviation of 2.
Using the above information, find x such that P(X>x)=0.05; find x such that P(X What is the breakdown of this problem? Help!
Thank You!
Click here to see answer by stanbon(75887)

Question 581280: Budget ($) in millions - Gross($)in millions
.25 - 12.006
.325 - 47
3.9 - 198.571
6 - 181.28
6.4 - 36.9
8 - 107.93
10 - 138.339
12 260
15 - 103.001
17 - 72.219
18.5 - 81.843
20 - 242.374
22 - 217.631
25 - 96.067
35 - 56.876
39 - 197.171
45 - 20.1
50 - 147.54
50 - 48.265
55 - 68.75
A) BRIEFLY CHARACTERIZE THE CORRELATION COEFFICIENT
B) THE EQUATION OF THE REGRESSION LINE CALCULATED ON THESE VALUES IS GROSS INCOME= 123.44-.536 BUDGET. USE THE REGRESSION LINE TO PREDICT THE GROSS INCOME FOR A MOVIE WITH BUDGET 30 MILLION DOLLARS
C) EXPLAIN WHETHER OR NOT YOU THINK THIS IS A REASONABLE PREDICTION. please help me!
Click here to see answer by KMST(5328)

Question 581324: If the claim says that the population mean is greater than 200 and the sample mean is 215, we can say that the claim is true even without a formal test
what is wrong with this statement

Click here to see answer by stanbon(75887)

Question 581303: how many ways can two republicans, one democrat, and one independent be chosen from nine republicans, five democrats, and two independents to fill 4 positions?
Click here to see answer by stanbon(75887)

Question 581338: What are the odds that two people would pick the same seven
books from a list of 150 to read?
Click here to see answer by stanbon(75887)

Question 581330: find the probability P(Z<0.37) using standard normal distribution.

Click here to see answer by stanbon(75887)

Question 581282: Construct the five number summary and a box plot for the following gas mileasges per gallon of various company cars: 22 18 13 28 30 12 38 22 30 39 20 18 14 16 10.
When I did the math I got my 5 numbers to be 10 14 19 30 39... Is this correct?! And also could I get help with drawing the box?! Thank you :)
Click here to see answer by stanbon(75887)

Question 581320: Using data from Boston, Massachusetts, a test of independence is run on the claim that ice cream sales per month and the number of car wrecks per month are independent. The claim is rejected.
Using number of car wrecks as the x variable and ice cream sales as the y variable, an r value of r=0.923 is then computed and shown to exceed the critical value for this data. The data is double checked and verified. This shows that car wrecks cause ice cream sales.
NOTE: While this specific r-value is made up, this general pattern has been shown in several real world data sets involving ice cream sales and number of car wrecks in major cities on the east coast of the United States.

***I saw that this question has been asked by another student on Algebra.com however I really did not understand the justification that was given. I am supposed to explain what is wrong and why it is wrong.
Click here to see answer by stanbon(75887)

Question 581358: When you buy a ticket there is a .0995 probability that someone will not show up for a flight. An agent for an airline wants to know what the probability is that there will not be enough seats on the plane if he sells 24 tickets for a flight but has only 22 seats. Based on the results, should the agent be concerned?
Click here to see answer by stanbon(75887)

Question 581379: I'm not sure which approach is correct for a probability question:
The letters of the word "fantastic" are written on cards and placed in a bag. Two cards are selected (without replacement). What is the probability that "at" will be selected. It seems order matters so my first thought was to multiply probabilities of "a" [2/9) and "t" [2/8] giving me 1/18. Then I thought perhaps I should be counting total eligible letters [4/9] x [3/8] resulting in 1/6. Which is correct?
Click here to see answer by stanbon(75887)

Question 581390: Defective
Suppose that a company determines if it will accept a shipment of 15 items by sampling 5 of the items for close inspection. Suppose that 4 of the items in the shipment are defective.
Referring to Defective, find the standard deviation of the number of defective items.
I think the way to do this problem is npq to get the variance and then find the square root to get the standard deviation. (5)(.8)(.2)=.8 then the square root is .8944
Click here to see answer by stanbon(75887)

Question 581393: Cans of classic Coke are filled so that the mean is 12.0 ounces with a standard deviation of 0.1 ounces. Find the probability that
a) a single can will have 12.2 or more ounces
b) a sample of 36 cans will have 12.2 or more ounces
c) Explain the difference in the answers for parts a and b
Any help would be awesome.
Thank you
Rae
Click here to see answer by stanbon(75887)

Question 581394: The mean SAT math reasoning score in 2009 was 515.3 with a standard deviation of 114.1. An educational psychologist believes that students who take at least 4 years of English in high school perform better on the exam. To test the hypothesis, she obtains a random sample of 40 student (with 4 years of English) and their mean score was 540. Test the claim at "alpha" = 0.05.
I am so lost on this one.
Thank you
Click here to see answer by stanbon(75887)

Question 581465: At a local college, times for running the mile are approximately normally distributed with a mean of 4.5 minutes and a standard deviation of 0.3 minutes. What is the probability that a randomly selected time will be less than 4 minutes?
Thanks again.
Click here to see answer by dfrazzetto(283)

Question 581466: Scores on a test are approximately normally distributed with a mean of 70 and a standard deviation of 9. The teacher wants to give A's to the top 10% of students and B's to the next 23%. What is the bottom cut-off for a B grade? Round to the nearest whole number.
My answer = 76
Thank you very much!
Click here to see answer by stanbon(75887)

Question 581464: Which score has the better relative position: a score of 49 on a test for which the mean is 41 and the standard deviation is 8, a score of 5.8 on a test for which the mean is 5 and the standard deviation is 0.7, or a score of 491.6 on a test for which the mean is 467 and the standard deviation is 41?
My answer = A score of 5.8
Thanks...you're the best!
Click here to see answer by stanbon(75887)

Question 581463: Elizabeth and Ann skate for their college speed skating team. In the last race, Elizabeth skated the 500 meter race in 60 seconds. The average for this race is 65 seconds with a standard deviation of 4.0 seconds. Angela skated the 1,000 meter race in 132 seconds. The average race for this race is 140 seconds with a standard deviation of 10.0 seconds. Find the z-score for each skater. Relatively speaking, which skater had the faster time?
My answer = -1.2, -0.8; Angela faster skater
Thank you.
Click here to see answer by stanbon(75887)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020, 16021..16065, 16066..16110, 16111..16155, 16156..16200, 16201..16245, 16246..16290, 16291..16335, 16336..16380, 16381..16425, 16426..16470, 16471..16515, 16516..16560, 16561..16605, 16606..16650, 16651..16695, 16696..16740, 16741..16785, 16786..16830, 16831..16875, 16876..16920, 16921..16965, 16966..17010, 17011..17055, 17056..17100, 17101..17145, 17146..17190, 17191..17235, 17236..17280, 17281..17325, 17326..17370, 17371..17415, 17416..17460, 17461..17505, 17506..17550, 17551..17595, 17596..17640, 17641..17685, 17686..17730, 17731..17775, 17776..17820, 17821..17865, 17866..17910, 17911..17955, 17956..18000, 18001..18045, 18046..18090, 18091..18135, 18136..18180, 18181..18225, 18226..18270, 18271..18315, 18316..18360, 18361..18405, 18406..18450, 18451..18495, 18496..18540, 18541..18585, 18586..18630, 18631..18675, 18676..18720, 18721..18765, 18766..18810, 18811..18855, 18856..18900, 18901..18945, 18946..18990, 18991..19035, 19036..19080, 19081..19125, 19126..19170, 19171..19215, 19216..19260, 19261..19305, 19306..19350, 19351..19395, 19396..19440, 19441..19485, 19486..19530, 19531..19575, 19576..19620, 19621..19665, 19666..19710, 19711..19755, 19756..19800, 19801..19845, 19846..19890, 19891..19935, 19936..19980, 19981..20025, 20026..20070, 20071..20115, 20116..20160, 20161..20205, 20206..20250, 20251..20295, 20296..20340, 20341..20385, 20386..20430, 20431..20475, 20476..20520, 20521..20565, 20566..20610, 20611..20655, 20656..20700, 20701..20745, 20746..20790, 20791..20835, 20836..20880, 20881..20925, 20926..20970, 20971..21015, 21016..21060, 21061..21105, 21106..21150, 21151..21195, 21196..21240, 21241..21285, 21286..21330, 21331..21375, 21376..21420, 21421..21465, 21466..21510, 21511..21555, 21556..21600, 21601..21645, 21646..21690, 21691..21735, 21736..21780, 21781..21825, 21826..21870, 21871..21915, 21916..21960, 21961..22005, 22006..22050, 22051..22095, 22096..22140, 22141..22185, 22186..22230, 22231..22275, 22276..22320, 22321..22365, 22366..22410, 22411..22455, 22456..22500, 22501..22545, 22546..22590, 22591..22635, 22636..22680, 22681..22725, 22726..22770, 22771..22815, 22816..22860, 22861..22905, 22906..22950, 22951..22995, 22996..23040, 23041..23085, 23086..23130, 23131..23175, 23176..23220, 23221..23265, 23266..23310, 23311..23355, 23356..23400, 23401..23445, 23446..23490, 23491..23535, 23536..23580, 23581..23625, 23626..23670, 23671..23715, 23716..23760, 23761..23805, 23806..23850, 23851..23895, 23896..23940, 23941..23985, 23986..24030, 24031..24075, 24076..24120, 24121..24165, 24166..24210, 24211..24255, 24256..24300, 24301..24345, 24346..24390, 24391..24435, 24436..24480, 24481..24525, 24526..24570, 24571..24615, 24616..24660, 24661..24705, 24706..24750, 24751..24795, 24796..24840, 24841..24885, 24886..24930, 24931..24975, 24976..25020, 25021..25065, 25066..25110, 25111..25155, 25156..25200, 25201..25245, 25246..25290, 25291..25335, 25336..25380, 25381..25425, 25426..25470, 25471..25515, 25516..25560, 25561..25605, 25606..25650, 25651..25695, 25696..25740, 25741..25785, 25786..25830, 25831..25875, 25876..25920, 25921..25965, 25966..26010, 26011..26055, 26056..26100, 26101..26145, 26146..26190, 26191..26235, 26236..26280, 26281..26325, 26326..26370, 26371..26415, 26416..26460, 26461..26505, 26506..26550, 26551..26595, 26596..26640, 26641..26685, 26686..26730, 26731..26775, 26776..26820, 26821..26865, 26866..26910, 26911..26955, 26956..27000, 27001..27045, 27046..27090, 27091..27135, 27136..27180, 27181..27225, 27226..27270, 27271..27315, 27316..27360, 27361..27405, 27406..27450, 27451..27495, 27496..27540, 27541..27585, 27586..27630, 27631..27675, 27676..27720, 27721..27765, 27766..27810, 27811..27855, 27856..27900, 27901..27945, 27946..27990, 27991..28035, 28036..28080, 28081..28125, 28126..28170, 28171..28215, 28216..28260, 28261..28305, 28306..28350, 28351..28395, 28396..28440, 28441..28485, 28486..28530, 28531..28575, 28576..28620, 28621..28665, 28666..28710, 28711..28755, 28756..28800, 28801..28845, 28846..28890, 28891..28935, 28936..28980, 28981..29025, 29026..29070, 29071..29115, 29116..29160, 29161..29205, 29206..29250, 29251..29295, 29296..29340, 29341..29385, 29386..29430, 29431..29475, 29476..29520, 29521..29565, 29566..29610, 29611..29655, 29656..29700, 29701..29745, 29746..29790, 29791..29835, 29836..29880, 29881..29925, 29926..29970, 29971..30015, 30016..30060, 30061..30105, 30106..30150, 30151..30195, 30196..30240, 30241..30285, 30286..30330, 30331..30375, 30376..30420, 30421..30465, 30466..30510, 30511..30555, 30556..30600, 30601..30645, 30646..30690, 30691..30735, 30736..30780, 30781..30825, 30826..30870, 30871..30915, 30916..30960, 30961..31005, 31006..31050, 31051..31095, 31096..31140, 31141..31185, 31186..31230, 31231..31275, 31276..31320, 31321..31365, 31366..31410, 31411..31455, 31456..31500, 31501..31545, 31546..31590, 31591..31635, 31636..31680, 31681..31725, 31726..31770, 31771..31815, 31816..31860, 31861..31905, 31906..31950, 31951..31995, 31996..32040, 32041..32085, 32086..32130, 32131..32175, 32176..32220, 32221..32265, 32266..32310, 32311..32355, 32356..32400, 32401..32445, 32446..32490, 32491..32535, 32536..32580, 32581..32625, 32626..32670, 32671..32715, 32716..32760, 32761..32805, 32806..32850, 32851..32895, 32896..32940, 32941..32985, 32986..33030, 33031..33075, 33076..33120, 33121..33165, 33166..33210, 33211..33255, 33256..33300, 33301..33345, 33346..33390, 33391..33435, 33436..33480, 33481..33525, 33526..33570, 33571..33615, 33616..33660, 33661..33705, 33706..33750, 33751..33795, 33796..33840, 33841..33885, 33886..33930, 33931..33975, 33976..34020, 34021..34065, 34066..34110, 34111..34155, 34156..34200, 34201..34245, 34246..34290, 34291..34335, 34336..34380, 34381..34425, 34426..34470, 34471..34515, 34516..34560, 34561..34605, 34606..34650, 34651..34695, 34696..34740, 34741..34785, 34786..34830, 34831..34875, 34876..34920, 34921..34965, 34966..35010, 35011..35055, 35056..35100, 35101..35145, 35146..35190, 35191..35235, 35236..35280, 35281..35325, 35326..35370, 35371..35415, 35416..35460, 35461..35505, 35506..35550, 35551..35595, 35596..35640, 35641..35685, 35686..35730, 35731..35775, 35776..35820, 35821..35865, 35866..35910, 35911..35955, 35956..36000, 36001..36045, 36046..36090, 36091..36135, 36136..36180, 36181..36225, 36226..36270, 36271..36315, 36316..36360, 36361..36405, 36406..36450, 36451..36495, 36496..36540, 36541..36585, 36586..36630, 36631..36675, 36676..36720, 36721..36765, 36766..36810, 36811..36855, 36856..36900, 36901..36945, 36946..36990, 36991..37035, 37036..37080, 37081..37125, 37126..37170, 37171..37215, 37216..37260, 37261..37305, 37306..37350, 37351..37395, 37396..37440, 37441..37485, 37486..37530, 37531..37575, 37576..37620, 37621..37665, 37666..37710, 37711..37755, 37756..37800, 37801..37845, 37846..37890, 37891..37935, 37936..37980, 37981..38025, 38026..38070, 38071..38115, 38116..38160, 38161..38205, 38206..38250, 38251..38295, 38296..38340, 38341..38385, 38386..38430, 38431..38475, 38476..38520, 38521..38565, 38566..38610, 38611..38655, 38656..38700, 38701..38745, 38746..38790, 38791..38835, 38836..38880, 38881..38925, 38926..38970, 38971..39015, 39016..39060, 39061..39105, 39106..39150, 39151..39195, 39196..39240, 39241..39285, 39286..39330, 39331..39375, 39376..39420, 39421..39465, 39466..39510, 39511..39555, 39556..39600, 39601..39645, 39646..39690, 39691..39735, 39736..39780, 39781..39825, 39826..39870, 39871..39915, 39916..39960, 39961..40005, 40006..40050, 40051..40095, 40096..40140, 40141..40185, 40186..40230, 40231..40275, 40276..40320, 40321..40365, 40366..40410, 40411..40455, 40456..40500, 40501..40545, 40546..40590, 40591..40635, 40636..40680, 40681..40725, 40726..40770, 40771..40815, 40816..40860, 40861..40905, 40906..40950, 40951..40995, 40996..41040, 41041..41085, 41086..41130, 41131..41175, 41176..41220, 41221..41265, 41266..41310, 41311..41355, 41356..41400, 41401..41445, 41446..41490, 41491..41535, 41536..41580, 41581..41625, 41626..41670, 41671..41715, 41716..41760, 41761..41805, 41806..41850, 41851..41895, 41896..41940, 41941..41985, 41986..42030, 42031..42075, 42076..42120, 42121..42165, 42166..42210, 42211..42255, 42256..42300, 42301..42345, 42346..42390, 42391..42435, 42436..42480, 42481..42525, 42526..42570, 42571..42615, 42616..42660, 42661..42705, 42706..42750, 42751..42795, 42796..42840, 42841..42885, 42886..42930, 42931..42975, 42976..43020, 43021..43065, 43066..43110, 43111..43155, 43156..43200, 43201..43245, 43246..43290, 43291..43335, 43336..43380, 43381..43425, 43426..43470, 43471..43515, 43516..43560, 43561..43605, 43606..43650, 43651..43695, 43696..43740, 43741..43785, 43786..43830, 43831..43875, 43876..43920, 43921..43965, 43966..44010, 44011..44055, 44056..44100, 44101..44145, 44146..44190, 44191..44235, 44236..44280, 44281..44325, 44326..44370, 44371..44415, 44416..44460, 44461..44505, 44506..44550, 44551..44595, 44596..44640, 44641..44685, 44686..44730, 44731..44775, 44776..44820, 44821..44865, 44866..44910, 44911..44955, 44956..45000, 45001..45045, 45046..45090, 45091..45135, 45136..45180, 45181..45225, 45226..45270, 45271..45315, 45316..45360, 45361..45405, 45406..45450, 45451..45495, 45496..45540, 45541..45585, 45586..45630, 45631..45675, 45676..45720, 45721..45765, 45766..45810, 45811..45855, 45856..45900, 45901..45945, 45946..45990, 45991..46035, 46036..46080, 46081..46125, 46126..46170, 46171..46215, 46216..46260, 46261..46305, 46306..46350, 46351..46395, 46396..46440, 46441..46485, 46486..46530, 46531..46575, 46576..46620, 46621..46665, 46666..46710, 46711..46755, 46756..46800, 46801..46845, 46846..46890, 46891..46935, 46936..46980, 46981..47025, 47026..47070, 47071..47115, 47116..47160, 47161..47205, 47206..47250, 47251..47295, 47296..47340, 47341..47385, 47386..47430, 47431..47475, 47476..47520, 47521..47565, 47566..47610, 47611..47655, 47656..47700, 47701..47745, 47746..47790, 47791..47835, 47836..47880, 47881..47925, 47926..47970, 47971..48015, 48016..48060, 48061..48105, 48106..48150, 48151..48195, 48196..48240, 48241..48285, 48286..48330, 48331..48375, 48376..48420, 48421..48465, 48466..48510, 48511..48555, 48556..48600, 48601..48645, 48646..48690, 48691..48735, 48736..48780, 48781..48825, 48826..48870, 48871..48915, 48916..48960, 48961..49005, 49006..49050, 49051..49095, 49096..49140, 49141..49185, 49186..49230, 49231..49275, 49276..49320, 49321..49365, 49366..49410, 49411..49455, 49456..49500, 49501..49545, 49546..49590, 49591..49635, 49636..49680, 49681..49725, 49726..49770, 49771..49815, 49816..49860, 49861..49905, 49906..49950, 49951..49995, 49996..50040, 50041..50085, 50086..50130, 50131..50175, 50176..50220, 50221..50265, 50266..50310, 50311..50355, 50356..50400, 50401..50445, 50446..50490, 50491..50535, 50536..50580, 50581..50625, 50626..50670, 50671..50715, 50716..50760, 50761..50805, 50806..50850, 50851..50895, 50896..50940, 50941..50985, 50986..51030, 51031..51075, 51076..51120, 51121..51165, 51166..51210, 51211..51255, 51256..51300, 51301..51345