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

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

Question 1203815: Three machines turn out all the products in a factory, with the first machine producing 10% of the products, the second machine 15%, and the third machine 75%. The first machine produces defective products 6% of the time, the second machine 15% of the time and the third machine 8% of the time. What is the probability that a non-defective product came from the second machine? (Round your answer to four decimal places.
Click here to see answer by ikleyn(52777)

Question 1203813: An urn contains 4 white balls and 6 red balls. A second urn contains 6 white balls and 4 red balls. An urn is selected, and a ball is randomly drawn from the selected urn. The probability of selecting the first urn is 0.8. If the ball is white, find the probability that the second urn was selected.
Click here to see answer by greenestamps(13198)

Question 1203817: Assume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find P31, the 31-percentile. This is the temperature reading separating the bottom 31% from the top 69%.
Click here to see answer by ikleyn(52777)

Question 1203830: milu is rolling a 6 sided die. She needs to roll a 6 to be able to begin playing a board game. She keeps rolling until she rolls a 6.
a) What is the probability she doesn't roll a 6 until her second attempt?
b) what is the probability she doesn't roll a 6 until her second attempt?
Click here to see answer by ikleyn(52777)

Question 1203831: milu is rolling a 6 sided die. She needs to roll a 6 to be able to begin playing a board game. She keeps rolling until she rolls a 6.
a) What is the probability she doesn't roll a 6 until her second attempt?
b) what is the probability she doesn't roll a 6 until her Third attempt?
Click here to see answer by ikleyn(52777)

Question 1203821: Company XYZ know that replacement times for the quartz time pieces it produces are normally distributed with a mean of 15.9 years and a standard deviation of 1.4 years. Find the probability that a randomly selected quartz time piece will have a
replacement time less than 12.1 years? If the company wants to provide a warranty so that only 0.9% of the quartz time pieces will be replaced before the warranty expires, what is the time length of the warranty?

Click here to see answer by ikleyn(52777)

Question 1203844: A bag contains 1 gold marbles, 8 silver marbles, and 21 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $4. If it is silver, you win $2. If it is black, you lose $1.
What is your expected value if you play this game?

Click here to see answer by math_tutor2020(3816)

Question 1203841: The frequency distribution below summarizes the home sale prices in the city of Summerhill for the month of June. Determine the width of each class.
Click here to see answer by math_tutor2020(3816)

Question 1203834: An urn contains 3 white balls and 7 red balls. A second urn contains 8 white balls and 2 red balls. An urn is selected, and the probability of selecting the first urn is 0.2. A ball is drawn from the selected urn and replaced. Then another ball is drawn and replaced from the same urn. If both balls are white, what are the following probabilities? (Round your answers to three decimal places.)
(a) the probability that the urn selected was the first one
(b) the probability that the urn selected was the second one
Click here to see answer by ikleyn(52777)

Question 1203812: An urn contains 3 white balls and 7 red balls. A second urn contains 8 white balls and 2 red balls. An urn is selected, and the probability of selecting the first urn is 0.2. A ball is drawn from the selected urn and replaced. Then another ball is drawn and replaced from the same urn. If both balls are white, what are the following probabilities? (Round your answers to three decimal places.)
(a) the probability that the urn selected was the first one

(b) the probability that the urn selected was the second one

Click here to see answer by ikleyn(52777)

Question 1203846: Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places.
P(X<5), n=7, p=0.3
Click here to see answer by MathLover1(20849)

Question 1203851: A die is rolled. Find the probability of the given event. Round all answers to 4 decimals.
(a) The number showing is a 6;
The probability is :

(b) The number showing is an even number;
The probability is :

(c) The number showing is greater than 2;
The probability is :

Click here to see answer by ikleyn(52777)

Question 1203848: The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 56 ounces and a standard deviation of 3 ounces.
Use the Empirical Rule.
Suggestion: sketch the distribution in order to answer these questions.
a) 68% of the widget weights lie between
and

b) What percentage of the widget weights lie between 50 and 59 ounces?
%
c) What percentage of the widget weights lie below 65 ?
%
Click here to see answer by Theo(13342)

Question 1203854: Lucien had 400 fifty cents coins. He used 1/8 of the coins on Friday. On Saturday, he used 1/7 of the coins that was left on Friday. On Sunday, Lucien used 1/5 of the coins that was left on Saturday.
a. What was the number of coins that was left at the end of Friday?
b. What was the value of coins left at the end of Sunday?

Click here to see answer by SCrappingDude(6)

Question 1203856: The probability density of a random variable X is given in the figure below.
From this density, the probability that X > 1.38 or X < 0.26 is
Click here to see answer by ikleyn(52777)

Question 1203867: The mean price paid is $1400 and the standard deviation is $110.
What is the approximate percentage of buyers who paid between $1290 and $1400?
%
What is the approximate percentage of buyers who paid between $1290 and $1510?
%
What is the approximate percentage of buyers who paid between $1180 and $1400?
%
What is the approximate percentage of buyers who paid less than $1180?
%
What is the approximate percentage of buyers who paid less than $1070?
%
What is the approximate percentage of buyers who paid between $1070 and $1400?
%
Click here to see answer by Theo(13342)

Question 1203853: Suppose you are playing a game that involves rolling a 20-sided die. Before the game begins, you name a number called the threshold from 0 to 19. Then you roll the die until you exceed your threshold T. You have to pay $1 per roll and you get paid whatever is shown on the die at the end. What is the threshold that maximizes the expected profit?
example: T=7; roll 4, 2, 11. profit = $11- $3=$8.
Click here to see answer by ikleyn(52777)

Question 1203803: A discrete random variable has pdf f(x).
(a) If f(x) = k(1/2)^x for x= 1, 2, 3, and zero otherwise, find k.
(b) Is a function of the form f(x) = k[(1/2)^x - 1/2] for x = 0, 1, 2 a pdf for any k?
Click here to see answer by math_tutor2020(3816)

Question 1203902: Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $8. If you roll a 4 or 5, you win $3. Otherwise, you pay $4.

Click here to see answer by MathLover1(20849)

Question 1203901: You measure 45 backpacks' weights, and find they have a mean weight of 49 ounces. Assume the population standard deviation is 14.8 ounces. Based on this, what is the maximal margin of error associated with a 95% confidence interval for the true population mean backpack weight.
Give your answer as a decimal, to two places

ounces
Click here to see answer by Theo(13342)

Question 1203912: Two machines turn out all the products in a factory, with the first machine producing 57% of the product and the second machine producing the rest. The first machine produces defective products 6% of the time and the second machine 2% of the time. What is the probability that a part made in this factory is not defective? (Enter answer as a decimal with at least 4 correct decimal places)

Click here to see answer by math_tutor2020(3816)

Question 1203897: A manufacturer produces a commodity where the length of the commodity has approximately normal distribution with a mean of 7.8 inches and standard deviation of 2.6 inches. If a sample of 49 items are chosen at random, what is the probability the sample's mean length is greater than 8.8 inches? Round answer to four decimal places.
Click here to see answer by Theo(13342)

Question 1203889: The lengths of pregnancies in a small rural village are normally distributed with a mean of 270 days and a standard deviation of 15 days. A distribution of values is normal with a mean of 270 and a standard deviation of 15.
What percentage of pregnancies last fewer than 257 days?
P(X < 257 days) = %
Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign). Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Click here to see answer by Theo(13342)

Question 1203929: Customer at TAB are charged for the amount of salad they take. Sampling suggests that the amount of salad take is uniformly distributed between 5 ounces and 15 ounces. Let X=salad plate filling weight. 1. Find the probability density of function of X. 2. What is the probability that a Customer will take between 12 and 15 ounces of salad. 3. What is the probability that a Customer will take fewer that 5 ounces of salad. 4 fine E(X) and Var (X).
Click here to see answer by ikleyn(52777)

Question 1203935: At an awards ceremony, nine women and seven men are each to receive an award and are to be presented with their award one at a time. Two of the awards are to be first given to two of the women, and then the remaining awards will alternate between men and women. How many ways can this be done?

Click here to see answer by MathLover1(20849)

Question 1203892: Let X be a continuous random variable with density function
f(x) = { theta*x + 3/2*theta^{3/2}*x^2, for 0 < x < 1/sqrt( theta ); 0, otherwise }
where theta > 0. What is the expected value of X?
Click here to see answer by math_tutor2020(3816)

Question 1203950: A CBS News poll conducted June 10 and 11, 2006, among a nationwide random sample of 651 adults, asked those adults about their party affiliation (Democrat, Republican or none) and their opinion of how the US economy was changing ("getting better," "getting worse" or "about the same"). The results are shown in the table below.
better same worse
Republican 38 104 44
Democrat 12 87 137
none 21 90 118

P(Republican) =
0.2857

P(worse) =
0.4593

P(worse|Republican) =

P(Republican|worse) =

P(Republican and worse) =
Click here to see answer by ikleyn(52777)

Question 1203949: A CBS News poll conducted June 10 and 11, 2006, among a nationwide random sample of 651 adults, asked those adults about their party affiliation (Democrat, Republican or none) and their opinion of how the US economy was changing ("getting better," "getting worse" or "about the same"). The results are shown in the table below.

P(Republican) =
0.2857

P(worse) =
0.4593

P(worse|Republican) =

P(Republican|worse) =

P(Republican and worse) =
Click here to see answer by ikleyn(52777)

Question 1203955: A committee of 6 U.S. senators is to be formed with 3 Democrats and 3 Republicans. In how many ways can this be done if there are 56 Democratic senators and 44 Republican senators?

Click here to see answer by MathLover1(20849)

Question 1203951: If sick-leave time X used by employees of a company in one month is (very roughly) normal with mean 1000 hours and standard deviation 100 hours, how much time t should be budgeted for sick leave during the next month if t is to be exceeded with probability of only 20%.

Click here to see answer by ikleyn(52777)

Question 1203972: The manager of a computer retail store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 4.3 years and a standard deviation of 0.6 years. He then randomly selects records on 54 laptops sold in the past and finds that the mean replacement time is 4.1 years.
Find the probability that 54 randomly selected laptops will have a mean replacement time of 4.1 years or less. Round your answer to four decimal places.
Click here to see answer by Theo(13342)

Question 1203804: A discrete random variable X has a pdf of the form f(x) = c(8 - x) for x = 0, 1, 2, 3, 4, 5, and zero otherwise.
(a) Find the constant c.
(b) Find the CDF, F(x).
(c) Find P[X > 2]
(d) Find E(X).
Click here to see answer by Edwin McCravy(20054)

Question 1203981: A study of 800 homeowners in a certain area showed that the average value of the homes was
$82,000, and the standard deviation was $5000. If 50 homes are for sale, find the probability
that the mean of the values of these homes is greater than $83,500.
Click here to see answer by Theo(13342)

Question 1203810: A random variable X has the pdf
x^2 if 0 < x ≤ 1
f(x) = 2/3 if 1 < x ≤ 2
0 otherwise
(a)Find the median of X.
(b)Sketch the graph of the CDF and show the position of the median on the graph.
Click here to see answer by Edwin McCravy(20054)

Question 1203983: If you draw a card with a value of two or less from a standard deck of cards, I will pay you $317
. If not, you pay me $24
. (Aces are considered the highest card in the deck.)
Step 1 of 2 : Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.

Click here to see answer by MathLover1(20849)

Question 1203979: The distribution of Master's degrees conferred by a university is listed in the table.
(assume that a student majors in only one subject)
Major Frequency
Mathematics 128
English 288
Engineering 86
Business 276
Education 222
What is the probability that a randomly selected student with a Master's degree did NOT major in Mathematics?
Round your answer to three decimal places.

Click here to see answer by ikleyn(52777)

Question 1203809: A random variable X has a CDF such that
x/2 0 < x ≤ 1
F(x) =
x-1/2 1 < x ≤ 3/2
(a)Graph F(x).
(b)Graph the pdf f(x).
(c)Find P[X ≤ 1/2].
(d)Find P[X ≥ 1/2].
(e)Find P[X ≤ 1.25].
(f)What is P[X = 1.25]?
Click here to see answer by Edwin McCravy(20054)

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