Tutors Answer Your Questions about Probability-and-statistics (FREE)
Question 79346: Mr. Thibodeaux is teaching probability to his class of 48 students. He has 12 decks of cards and 18 pairs of six-sided dice. He wants to divide his class into equal-sized groups. He plans to give each group the same number of decks of cards and the same number of pairs of dice. He also wants to use all of his manipulatives and to have no more than 20 students in each group. How many equal-sized groups are possible? Explain results please.
Click here to see answer by stanbon(75887)  |
Question 79369: According to the CDC, if one member of the household contracts the
chickenpox, 90% of family member who have never had the disease or a
vaccine will contract the chickenpox. Suppose four members are exposed
for the first time. What is the probability that three or fewer family
members contract the chickenpox?
Click here to see answer by stanbon(75887) |
Question 79663: Please show me step by step answers on how to solve the 4 problems. Thankyou. It will be greatly appreciated.
Question 1
A researcher wants to estimate the proportion of students at York College who will choose Computer Science as their major in Spring 2008. She wants to be within 5.3% of the actual popultaion proportion and have a 95% level of significance. In a preliminary survey of 42 students 29 said they wanted to take Computer Science in 2008. What is the minimum sample size that she will require? Round final answer up to the next whole number.
Question 2
A fast food restaurant claims that the mean waiting time is not equal to 3 minutes. A random sample of 45 customers revealed a mean waiting time of 3.3 minutes with a standard deviation of 0.7 minutes. Test the restaurants claim at a, a=0.05 level of significance. Assume that the population is normally distributed, and the population standard deviation is 0.7. Use the P-value method.
Question 3: Hypothesis Testing for Proportions.
A researcher at York claims that for Mathematics courses the proportion of grades B or higher was more than 33.0%. In a random sample of 100 grades issued in the year 2006 there were 27 F's, 15 D's, 22 C's, 14 B's, 22 A's. At a=0.10 test the researcher's claim.
Use "rejestion region" claim.
Question 4: Determining sample size
A. A large public university wants to estimate the average(mean) teaching experience of it's faculty. A preliminary random sample of 20 faculty yields a standard deviation of s=2.5 years.
The dean wants to be 95% confident that the sample mean does not have a maximum error of estimate of more than 1.6 years. (Hint: this is maximum error of estimate E). How large of a sample should she use? Use the preliminary sample sample standard deviation as an approximation of the population standard deviation. ROund up to the next whole number.
B. If she decides on a maximum error of estimate of 1.8years. and a level of significance of 95% how large of a sample should she use? Round up to next whole number.
Click here to see answer by stanbon(75887) |
Question 79661: Can someone solve these problems step by step for me. I got them wrong on my last test. ThanYou It will be greatly appreciated.
Question 1 : Confidence Intervals for the Mean
A random sample of 17 students were tested on the SAT english exam. If the mean score was 653.4 with a standard deviation of 135.457, find the 90% confidence interval for the popultation mean. Assume that the population standard deviation in unknown. Assume the scores are approximately normally distributed. Choose the appropriate distribution and state the reason(s) for your choice.Round off your answer to 1 decimal place.
Question 2 : Confidence Interval for a Population Proportion
In a random sample of 50 students enrolled in remedial math courses 21 passed the MAT test by the end of the semester.
A. Calculate the confidence interval for the population percentage of all students in remedial math courses who passed the MAT exam by the end of the semester. Use a 90% level of significance. Round off your final answer to 1 decimal place in percent.
B. If the margin of error is changed to 13.50% and the confidence level remains the same as in Part a, what is the minimum sample size required to estimate the population proportion of students who passed the MAT test? Use the proportions from Part a. Round up the sample size.
Question 3: Hypothesis Testing for the Mean
A sociologist wants to determine if the number of individuals per family unit the national average of 2.9. She interviews 31 randomly selected families in a large apartment complex and obtains a mean of 3.1 individuals per family unit with a standard deviation of 0.80. Test the claim that the mean number of individuals per family unit is less than 2.9. Use a significance level of 0.05. Assume that the population has a normal distribution and that the population standard deviation is unknown. You must decide whether to use the z-test or t-test. If you use the z-test use the P-value method.
Question 4: Confidence intervals for Variance and Standard Deviation
Suppose you are given a sample set of data consisting of 17 body temperatures, with s=1.02. Assume that body temperatures are normally distributed . Find the 95% confidence interval for the population variance 0^2. Round off to 2 decimal places.
Click here to see answer by stanbon(75887) |
Question 79977: Preface: You are going to draw a random marble from a bag containing 5 red marbles, 8 green marbles and two blue marbles.
Question: What is the probability that you draw a red marble?
What are the odds that you draw a blue marble?
Click here to see answer by Edwin McCravy(20054)  |
Question 80042: during a difficult release move, a gymnast has fallen from the parallel bars 2 of the 12 competitions this season. the state meet is next week. what is the probability that she will successfully complete the release move?
Click here to see answer by stanbon(75887) |
Question 80068: Question 1
A. A large public university want to estimate the average (mean) teaching experience of it's faculty. A preliminary random sample of 20 faculty yields a standard deviation of s=2.5 years. The dean wants to be 95% confident that the sample does not have a maximum error of estimate of more than 1.6 years. (Hint: this is maximum error of estimate E). How large of a sample should she use? Use the preliminary sample standard deviation as an approximation of the population standard deviation. Round up to next whole number.
B. If she decides on a maximum error of 1.8 years and a level of significance of 95% how large of a sample should she use? Round up to next whole number.
Question 2
Suppose you are given a sample set of data consisting of 17 body temperatures, with s= 1.02. Assume that body temperatures are normally distributed. Find the 95% confidence interval for the population variance. Round off 2 decimal places.
Click here to see answer by stanbon(75887) |
Question 80063: during a game, the pittsburgh steelers converted 4 of 12 fourth downs into first downs. with only minutes left in the game, it is fourth down again and they must make a first down to continue their drive. what is the probability that they will make the first down?
Click here to see answer by stanbon(75887) |
Question 80062: Question 1
A fast food restaurant claims that the mean time is not equal to 3 minutes. A random sample of 45 customers revealed a mean waiting time of 3.3 minutes with a standard deviation of 0.7 minutes. Test the restaurants claim at a, a= 0.05 level of significance. Assume that the population is normally distributed, and the population standard deviation is 0.7. Use the P-value method.
Question 2
A researcher at NYU claims that for Mathematics courses the proportion of grades B or higher was more than 33.0%. In a random sample of 100 grades issued in the year 2006 there were 27 F's, 15 D's, 22 C's, 14 B's, 22 A's. At a=0.10 test the researcher's claim.
Question 3
A sociologist wants to determine if the number of individuals per family unit the national average of 2.9. She interviews 31 randomly selected families in a large apartment complex and obtains a mean of 3.1 individuals per family unit with a standard deviation of 0.80. Test the claim that the mean number of individuals per family unit is less than 2.9. Use a significance level of 0.05. Assume that the population has a normal distribution and that the population standard deviation is unknown. Decide to use the t-test or z-test. If you use the z-test use the P-value method.
Click here to see answer by stanbon(75887) |
Question 80196: There are 13 green, 15 yellow, and 55 blue jellbeans in a jar at the start of a party. terri ate 12blue and two green jellybean from jar. What is the probability of picking a yellow jellybean at radom after Mike ate his?
Click here to see answer by muffinmix101(2) |
Question 80435: During the hunting season Ken arms himself with his bow and arrows(30% of the time) or his rifle(70% of the time).
If Ken uses his archery skills to bag his game the probabilities of success are: turkey=60%, deer=80%, and bear 30%
However if he uses his rifle, his success probabilities rise to: turkey=80%, deer 90%, and bear 60%
What is the probability of Ken making a triple kill this hunting season?
a. 0.0432
b. 0.3024
c. 0.3456
d. 0.6544
e. none of the above
Click here to see answer by Edwin McCravy(20054) |
Question 80681: I sent this one before but made some misstakes sorry. In the question u is for population mean and o is for Population standards deviation thank you .
Let X be a normally distributed random variable with u=100 and o=15 . The probability that is between 80 and 120 is (to the nearest whole percent)
a. 8 % b. 82 % c. 91% d. answer not listed
Click here to see answer by stanbon(75887) |
Question 80677: looking for another opinion on this question
What is the minimum percentage of data in any frequency distribution that lies within three standard deviations of its mean?
a. 67% b. 75%
c. 25% d. answer not listed.
I think it is b but not sure thank you for the help
Click here to see answer by rapaljer(4671)  |
Question 80686: looking for some help and need it too. one question has me stoped dead and two others just want someone to check my work thank you.
Among 100 people randomly chosen in a survey, 10 stated that they believed that the elected representatives are honest most of the time. The approximate 95% confidence interval for the percentage of the population who believe that such people are honest most of the time is
For questions 11 and 12 use the table immediately below. The table shows the number of smokers and nonsmokers by gender among 210 randomly selected people.
Smokers Nonsmokers Totals
Male 30 60 90
Female 40 80 120
Totals 70 140 210
_____11. If a smoker is chosen at random, the probability that the person is male is
12. If a male is chosen at random, the probability that he is a smoker is
would like to get a nother look at 11 and 12 I think 11 is 30/70 and 12 is no answer with this data.
thank you for your time.
Click here to see answer by stanbon(75887) |
Question 80839: One card is selected from a deck of standard poker cards at random. Assume a typical deck of 52 totals cards numbered from 2 thru 10 and Jack thru Ace, such that there are 13 red hearts, 13 red diamonds, 13 black spades, and 13 black clubs. Find the probability the card is RED and LESS THAN 4 (that is, RED and 2 or 3 ONLY.
A. 1
B. 2/13
C. 1/13
D. 17/26
Click here to see answer by checkley75(3666) |
Question 80838: Assume there are 10 people taking this class. 3 recieve a grade of "A", 4 recieve a grade of "B" and 3 recieve a grade of "C". What are the odds that the next person to enter the class will recieve a grade of "B"?
A. 2:3
B. 3:2
C. 2:5
D. None of the above
Click here to see answer by checkley75(3666) |
Question 80842: Assume the following data set for points scored in a basketball game by a player Data Set: (12, 15, 20, 23, 29, 30). Assuming a standard normal distribution what would be the percentage of basketball games where the player should score more than 25 points?
A. 18.4%
B. 50%
C. 31.6%
D. 68.4%
Click here to see answer by stanbon(75887) |
Question 80846: not sure how to type this but here goes
Let a random sample be taken of size n = 100 from a population with known standard deviation of o = 20 . Suppose that the mean of the sample is X = 37 . The approximate 68% confidence interval for the mean, u , of the population from which the sample was drawn is
n = n
o = Population standard deviation
X = Sample mean
u = population mean
I need some help on this question and my key board is short some keys. I hope that you can help thank you mirna.
Click here to see answer by stanbon(75887) |
Question 80844: Looking for some help. this question is a smoker.
Among 100 people randomly chosen in a survey, 10 stated that they believed that the elected representatives are honest most of the time. The approximate 95% confidence interval for the percentage of the population who believe that such people are honest most of the time is
thank you for your time and help.
Click here to see answer by stanbon(75887) |
Question 80837: Assume there are 10 people taking this class. 3 recieve a grade of "A", 4 recieve a grade of "B" and 3 recieve a grade of "C". What is the empirical probability the next person to enter the class will recieve a grade of "A"?
A. 2/5
B. 3/11
C. 3:10
D. 3/10
Click here to see answer by stanbon(75887) |
Question 80907: At a fair run by local charity organization, it cost 50 cents to try ones luck in drawing an ace from a deck of 52 playing cards. What is the expected profit per customer, if they pay $4 if and only if a person draws an ace?
Click here to see answer by checkley75(3666) |
Question 80914: An artist entered two paintings(lighthouse, and Old catherdral) in the show. He feels that the probablities are 0.15, 0.18, 0.11, respectively, that he will sell the lighthouse, the old catherdral, or both. What is the probability that he will sell either of the two paintings?
Click here to see answer by stanbon(75887) |
Question 80942: looking for some help I need to type the question out because I an short some key on my key board.
Let a random sample be taken of size n=100 from a population with known standard deviation of o=20 . Suppose that the mean of the sample is X=37 . The approximate 68% confidence interval for the mean, u , of the population from which the sample was drawn is
n = n
o = population standard deviation
X = sample mean
u = population mean
thank you for you time and help.
Click here to see answer by stanbon(75887) |
Question 81009: The table below shows the number of tests taken by 30 randomly selected college sophomores
Number of tests taken Number of students
0 12
1 8
2 2
3 3
4 or more 5
_________________________________________________
If a student is selected at random, find the probability
a) the student has taken exactly two tests
b) the student has taken at least two tests
c) the student has taken at most three tests
d) the student has taken 3 or fewer tests
e) the student has taken one or two tests.
Click here to see answer by stanbon(75887) |
Question 81325: Please Help! This will be greatly appreciated. (Show Step by step solutions to these problems I got incorrect on my test)Thank You.
Question 1
A local bank says that the standard deviation for bank account balances is less than or equal to $2150.91. A random sample of size n=16 bank accounts reveals a standard deviation of s=$2129.61. Assume that the bank balances are normally distributed. Test the hypothesis that the standard deviation for bank accounts is less than or equal to $2150.91 at the a=0.05 significance level.
Question 2
The following represents the mean scores on the same set of 5 statistics exams given in Spring 2004 and Fall 2004. Test the claim that the mean scores for the Spring 2004 semester were not equal to the mean scores for Fall 2004 semester. Use a=0.05.
Spring 2004- Test 1= 48.7, Test 2= 68.9,Test 3= 75.2, Test 4= 94.3, Test 5= 98.7
Fall 2004- Test 1= 49.0, Test 2= 68.8, Test 3= 75.5, Test 4= 95.1, Test 5= 100.6
Question 3
An instructor wanted to test the effectiveness of a CALS (Computer Aided Learning System). Two classes were offered in Statistics I. One class used a CALS and the other used traditional methods. At the end of the two courses both classes were given the same final exam. The CALS class had 117 students and 19 of the class receives a grade of B or higher. The class taught using traditional methods had 143 students and 39 of the class receives a grade of B or higher. At a=0.05 can you conclude that the CALS produced a smaller proportion of students with a grade of B or higher.
Question 4
Test the claim that the difference between the mean salary for computer programmers and the mean salary for photographers in Wisconsin is not equal to 28,000. The results of a survey of randomly selected computer programmers and photographers in Wisconsin are shown in the figure below.
Use alpha= 0.01 and Rejection Region test. Testing a Difference other than zero.
Photographers and Computer Programmer Salaries
Computer programmers
x1= $52,400
s1= $8,290
n1= $31
Photographers
x2= $24,200
s2= $3,490
n2= $32
Click here to see answer by stanbon(75887) |
Question 81424: An electronic toy manufacturer uses a particular kind of quality test to check the toys. The test indicates defects in 85% of defective toys, but it also indicates defects in 2% of nondefective toys. The test indicates that toy A is defective. If 5% of toys have defects, what is the probability that toy A has a defect?
Click here to see answer by stanbon(75887) |
Question 82070: If Sally can paint a house in 4 hours and John can paint the same house in 6 hours, how long will it take to paint the same house together?
A. 2 hr. 24 min
B.3 hr. 12 min.
C. 3 hr. 44 min.
D. 4 hr. 10 min.
E. 4 hr. 33 min.
I tried to solve by dividing both of their times by 2 but that gave me 5 and it wasn't one of the answer choices. How would you solve this?
Click here to see answer by stanbon(75887) |
Question 82070: If Sally can paint a house in 4 hours and John can paint the same house in 6 hours, how long will it take to paint the same house together?
A. 2 hr. 24 min
B.3 hr. 12 min.
C. 3 hr. 44 min.
D. 4 hr. 10 min.
E. 4 hr. 33 min.
I tried to solve by dividing both of their times by 2 but that gave me 5 and it wasn't one of the answer choices. How would you solve this?
Click here to see answer by dolphinlover100(1) |
Question 82936: Can someone show me step by step the correct answer. Thanyou It will be greatly appreciated.
Question 1
The following represents the mean scores on the same set of 5 statistics exams given in Spring 2004 and Fall 2004. Test the claim that the mean scores for the Spring 2004 semester were greater than or equal to the mean scores for the Fall 2004 semester. Use a= 0.10
Spring 2004
Test 1 =46.0, Test 2= 47.1, Test 3= 55.7, Test 4= 58.2, Test 5= 62.4
Fall 2004
Test 1= 46.3, Test 2= 47.2, Test 3= 55.2, Test 4= 57.6, Test 5=63.6
Click here to see answer by stanbon(75887) |
Question 83092: Data Set #1
44, 35, 44, 22, 40, 40, 72, 21, 72, 70
Data Set #2
7.8, 4.9, 4.9, 3.8, 4.4, 7.1, 3.3, 7.6, 4.0, 3.1, 6.0
Find Mean, Median, Mode, Sum of squares, Variance, Standard Deviation,
Of Data Set #1 and Data Set #2.
Click here to see answer by Mona27(45) |
Question 83387: USE THE DIE AND SPINNER. IF THE RESULTS OF A SECOND INDEPENDENT EVENT DO NOT DEPEND ON THE RESULTS OF THE FIRST ,TWO EVENTS CAN OCCUR AT THE SAME TIME AND ARE CALLED INDEPENDENT EVENTS. TO FIND THE PROBABILTY OF TWO INDEPENDENTEVENTS, MULTIPLY THE PROBABILITS OF EACH EVENTP(A AND B) =P(A)X P(B). P(6AND GREEN MULTIPY1/6AND 2/5 TOGETHER THEN REDUCE THE FRACTION IF POSSIBLE .i don't no how to multiply these fractions please help me .thanks
Click here to see answer by Mona27(45) |
Question 83419: the following table lists how poerty level income cutoffs (in dollars) for a family of four have changed over time
year/income
1970/3968
1975/5500
1980/8414
1985/10989
1990/13359
1995/15569
2000/17603
Let x be the year, with x = 0 corresponding to 1970, and y be the income in thousands of dollars. (note: symbol weird E x = 105, Weird Ex^2 = 2275, weird Ey=75.402, Weird Ey^2 = 968.270792, wierd Exy = 1460.97)
A) PLOT THE DATA. DO THE DATA APPEAR TO LIE ALONG A SRAIGHT LINE?
B) CALCULATE TH ECOEFFICIENT OF CORRELATION. dOES YOUR RESULT AGREE WITH YOUR ANSWER IN PART a?
C)fIND THE EQUATION OF THE LEAST SQUARE LINE.
d) uSE YOUR ANSWER FROM PART c TO PREDICT THE POVERTY LEVEL IN THE YEAR 2015.
Click here to see answer by stanbon(75887) |
Question 83418: Decrease in Banks The number of banks in the United
States has dropped about 30% since 1992. The following
data are from a survey in which x represents the years
since 1900 and y corresponded to the number of banks, in
thousands, in the United States.†
n=10 the weird E symbol x^2 = 93,205
werid E x = 965 weird E xy = 9165.10
weird y = 95.3 weird y^2 = 920.47
a. Find an equation of the least squares line.
b. If the trend continues, how many banks will there be in
2004?
c. Find and interpret the coefficient of correlation.
Click here to see answer by stanbon(75887) |
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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, 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