Tutors Answer Your Questions about Probability-and-statistics (FREE)
Question 1197057: Hello! Please help me with this question:
There are 10 students with different designs of gloves. A professor asked them to put all their gloves in a box and he randomly selected 6 pieces of gloves. What is the probability that there is exactly one matching pair of gloves?
My initial solution to this problem is 6/60 = 1/10. But I'm not entirely sure about this. Can anyone help me? Thank you!
Click here to see answer by ikleyn(52778)   |
Question 1197057: Hello! Please help me with this question:
There are 10 students with different designs of gloves. A professor asked them to put all their gloves in a box and he randomly selected 6 pieces of gloves. What is the probability that there is exactly one matching pair of gloves?
My initial solution to this problem is 6/60 = 1/10. But I'm not entirely sure about this. Can anyone help me? Thank you!
Click here to see answer by ewatrrr(24785)  |
Question 1196927: The value of the Conference Board Index of 10 economic indicators in the United States could be approximated by the following function of time t in months since the end of December 2002.†
E(t) =
0.2t + 135 if 6 ≤ t ≤ 15
−0.2t + 141 if 15 < t ≤ 20.
(a)
Estimate
E(10), E(16), and E(20).
E(10) =
E(16) =
E(20) =
Interpret your answers.
E(10)
means in
---Select---
of the year
Correct:
the Conference Board Index was
.
E(16)
means in
---Select---
of the year
the Conference Board Index was
.
E(20)
means in
---Select---
of the year
the Conference Board Index was
.
(b)
Sketch the graph of E. Use your graph to estimate when the index first reached 138.
t =
(c)
Use technology to generate a table of values for E(t) with
t = 6, 7, , 20.
t 6 7 8 9 10
E(t)
t 11 12 13 14 15
E(t)
t 16 17 18 19 20
E(t)
Click here to see answer by MathLover1(20849)  |
Question 1197112: In a survey of nursing students pursuing a master's degree, 75 percent stated
that they expect to be promoted to a higher position within one month after
receiving the degree. If this percentage holds for the entire population, find,
for a sample of 15, the probability that the number expecting a promotion
within a month after receiving their degree is: 4pts each
(a) At last seven.
(b) No more than five.
(c) Between six and nine, inclusive.
(d) How many nurses would expect to see a proportion in the month after graduation?
Please explian option (d) with formula
Click here to see answer by ikleyn(52778) |
Question 1197125: An extract of a study conducted about the effects of a special class designed to aid students with
verbal skills is given below:
Each child was given a verbal skill test twice, both before and after completing a 4-week period
in the class. Let Y = score on exam at time 2 - score on exam at time 1. Hence, if the population
mean µ for Y is equal to 0, the class has no effect, on the average. For the four children in the
study, the observed values of Y are 8-5=3, 10-3=7, 5-2=3, and 7-4=3 (e.g. for the first child, the
scores were 5 on exam 1 and 8 on exam 2, so Y = 8-5=3). It is planned to test the null hypothesis
of no effect against the alternative hypothesis that the effect is positive, based on the following
results from a statistical software package:
Variable Number of cases Mean Standard Deviation Standard Error
Y 4 4.000 2.000 1.000
1.1.1 Set up the null and alternative hypotheses. (4)
1.1.2 Calculate the test statistic, and indicate whether the P-value was below 0.05, based on
using the appropriate table. (7)
1.1.3 Make a decision, using α = .05. Interpret. (4)
1.1.4 If the decision in (1.1.3.) is actually (unknown to us) incorrect, what type of error has
been made? What could you do to reduce the chance of that type of error?
(3)
1.1.5 True or false? When we make a decision using α = .05, this means that if the special class
is truly beneficial, there is only a 5% chance that we will conclude that it is not beneficial.
(3)
1.2 For a random sample of Harvard University psychology majors, the responses on political
ideology had a mean of 3.18 and standard deviation of 1.72 for 51 non-vegetarian students and
a mean of 2.22 and standard deviation of .67 for the 20 vegetarian students.
1.2.1 Defining appropriate notation, state the null and alternative hypotheses for testing
whether there is a difference between population mean ideology for vegetarian and nonvegetarian students. (4)
1.3 When we use statistical software to compare the means with a significance test, we obtain the
following printout:
Variance T DF Prob>|T|
Unequal 2.9146 41.9 0.006
1.3.1 Interpret the P-value, in context, based on its definition. (Note: You are not being asked
to make a decision at some α-level.) (5
Click here to see answer by ikleyn(52778) |
Question 1197114: question 1
Internet Shopping In a Gallup poll, 1025 randomly selected adults were surveyed and 29% of them
said that they used the Internet for shopping at least a few times a year.
a. Find the point estimate of the percentage of adults who use the Internet for shopping.
b. Find a 99% confidence interval estimate of the percentage of adults who use the Internet for
shopping.
c. If a traditional retail store wants to estimate the percentage of adult Internet shoppers in order to
determine the maximum impact of Internet shoppers on its sales, what percentage of Internet
shoppers should be used?
question 2
Sample Size for Mean IQ of Statistics Students The Weschler IQ test is designed so that the mean is
100 and the standard deviation is 15 for the population of normal adults. Find the sample size
necessary to estimate the mean IQ score of statistics students. We want to be 95% confident that our
sample mean is within 2 IQ points of the true mean. The mean for this population is clearly greater
than 100. The standard deviation for this population is probably less than 15 because it is a group
with less variation than a group randomly selected from the general population; therefore, if we use
σ = 15, we are being conservative by using a value that will make the sample size at least as large as
necessary. Assume then that σ = 15 and determine the required sample size.
question 3
Estimating Car Pollution In a sample of seven cars, each car was tested for nitrogen-oxide emissions
(in grams per mile) and the following results were obtained: 0.06, 0.11, 0.16, 0.15, 0.14, 0.08, 0.15
(based on data from the Environmental Protection Agency). Assuming that this sample is
representative of the cars in use, construct a 98% confidence interval estimate of the mean amount of
nitrogen-oxide emissions for all cars. If the Environmental Protection Agency requires that nitrogenoxide emissions be less than 0.165 grams mile, can we safely conclude that this requirement is
being met?
question 4
Comparing Waiting Lines
a. The listed values are waiting times (in minutes) of customers at the Jefferson Valley Bank, where
customers enter a single waiting line that feeds three teller windows. Construct a 95% confidence
interval for the population standard deviation σ.
6.5 6.6 6.7 6.8 7.1 7.3 7.4 7.7 7.7 7.7
b. The listed values are waiting times (in minutes) of customers at the Bank of Providence, where
customers may enter any one of three different lines that have formed at three teller windows.
Construct a 95% confidence interval for the population standard deviation σ.
4.2 5.4 5.8 6.2 6.7 7.7 7.7 8.5 9.3 10.0
Click here to see answer by ikleyn(52778) |
Question 1197137: 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<2)
, n=3, p=0.8
Click here to see answer by ikleyn(52778) |
Question 1197138: The number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM has a mean of 4. Calculate the probability of getting no more than 1 call between eight and nine in the morning. Round your answer to four decimal places.
Click here to see answer by ewatrrr(24785) |
Question 1197155: Based on a recent Gallup poll, 45% of Americans believe that the overall state of moral values in the United States is poor. Assume this percentage holds for the entire population.
For a random sample of 200 adult Americans, let X denote the number in the sample who do NOT believe that the overall state of moral values in the United States is poor.
Calculate the expected value of X. Round your answer to two decimal places.
Click here to see answer by ikleyn(52778) |
Question 1197156: According to flightstats.com, American Airlines flights from Dallas to Chicago are on time 78.2% of the time.
Suppose 15 of these flights are randomly selected and the number of on-time flights is recorded.
Calculate the probability that 9 or fewer of the selected flights were on time. Enter your answer as a decimal rounded to four decimal places.
Click here to see answer by ikleyn(52778) |
Question 1197159: The probability that a randomly selected patient who visits an emergency room (ER) will die within 1 year of the visit is 0.032.
A researcher obtains a random sample of 1000 recent ER visitors. It is safe to assume that the outcomes for each patient are independent of the other patients.
Calculate the standard deviation for the number of deaths in the next year amongst the 1000 patients in the sample. Round your answer to two decimal places.
Click here to see answer by ikleyn(52778) |
Question 1197158: An extract of a study conducted about the effects of a special class designed to aid students with
verbal skills is given below:
Each child was given a verbal skill test twice, both before and after completing a 4-week period
in the class. Let Y = score on exam at time 2 - score on exam at time 1. Hence, if the population
mean µ for Y is equal to 0, the class has no effect, on the average. For the four children in the
study, the observed values of Y are 8-5=3, 10-3=7, 5-2=3, and 7-4=3 (e.g. for the first child, the
scores were 5 on exam 1 and 8 on exam 2, so Y = 8-5=3). It is planned to test the null hypothesis
of no effect against the alternative hypothesis that the effect is positive, based on the following
results from a statistical software package:
Variable Number of cases Mean Standard Deviation Standard Error
Y 4 4.000 2.000 1.000
1.1.1 Set up the null and alternative hypotheses. (4)
Click here to see answer by ewatrrr(24785) |
Question 1197161: A coin is loaded so that heads is three times as likely as the tails. For 3 independent
tosses of the coin find the pmf of the total number of heads realized and the probability of
realizing at most 2 heads.
Click here to see answer by ikleyn(52778) |
Question 1197173: When two balanced dice are rolled, 36 equally likely outcomes are possible. Let X denote the sum of the dice. a) What are the possible values of the random variable X ? b) Use random-variable notation to represent the event that the sum of the dice is 7. c) Find P(X = 7). d) Find the probability distribution of X . Leave your probabilities in fraction form. e) Construct a probability histogram for X.
Click here to see answer by math_tutor2020(3816) |
Question 1197157: Clarinex-D is a medication whose purpose is to reduce the symptoms associated with a variety of allergies. In clinical trials of this medication, 5% of the patients in the study experienced insomnia as a side effect.
A random sample of 50 Clarinex-D users is obtained.
The probability that more than 4 people in the sample experience insomnia as a side effect is .
The probability that less than 2 people in the sample experience insomnia as a side effect is .
The probability that between 2 and 7 people in the sample, inclusive, experience insomnia as a side effect is .
Click here to see answer by ewatrrr(24785) |
Question 1197184: Of 41 bank customers depositing a check, 25 received some cash back.
a)Construct a 90 percent confidence interval for a proportion of all depositors who ask for cash back. (Round your answers to 4 decimal places.)
b) May normality of p be assumed?
Click here to see answer by math_tutor2020(3816) |
Question 1197180: The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of μ=22.25 mpg and a standard deviation of σ=1.50 mgp.
a) What is the standard error of X (with a line on top), the mean form a random sample of 36 fill-ups by one driver? (Round your answer to 4 decimal places.)
b) Within what interval would you expect the sample mean to fall, with 99 percent probability? (Round your answer to 4 decimal places.)
Click here to see answer by ewatrrr(24785) |
Question 1197197: Food Safety. The article cited research by the Food Marketing Institute, which indicates that 66% of consumers in the United States are confident that the food they buy is safe. Suppose that six consumers in the United States are randomly sampled and asked whether they are confident that the food they buy is safe. Determine the probability that the number answering in the affirmative is: a) exactly two. b) exactly four. c) at least two. d) Determine the probability distribution of the number of U.S. consumers in a sample of six who are confident that the food they buy is safe.
Click here to see answer by ewatrrr(24785) |
Question 1197201: Only 20% of a country's adults get enough leisure time exercise to achieve cardiovascular fitness. Choose 4 adults at random. Find the probabilities of the following. Enter your answer as a fraction or decimal rounded to three decimal places.
Click here to see answer by math_tutor2020(3816) |
Question 1197217: Color Blindness: According to the Medical College of Wisconsin Eye Institute, 9% of men are color blind. For four randomly selected men, determine the probability that:
a) none are color blind.
b) the first three are not color blind and the fourth is color blind.
c) exactly one of the four is color blind.
Click here to see answer by ikleyn(52778) |
Question 1197221: A truth serum given to a suspect is known to be 90 % reliable when the person is guilty and 99 % reliable when the person is innocent. If the suspect was selected from a group of suspects of which only 5% have ever committed a crime, and the serum indicates that he is guilty, what is the probability that he is innocent?
Click here to see answer by math_tutor2020(3816) |
Question 1197223: A normal distribution has 𝜇 = 26 and 𝜎 = 5.
(a) Find the z score corresponding to
x = 21.
(b) Find the z score corresponding to
x = 40.
(c) Find the raw score corresponding to
z = −2.
(d) Find the raw score corresponding to
z = 1.1.
Click here to see answer by MathLover1(20849) |
Question 1197238: A marriage counselor has traditionally seen that the proportion of all married couples for whom her communication program can prevent divorce is . After making some recent changes, the marriage counselor now claims that her program can prevent divorce in more than of married couples. In a random sample of married couples who completed her program, of them stayed together. Based on this sample, is there enough evidence to support the marriage counselor’s claim at the level of significance?
Click here to see answer by math_tutor2020(3816) |
Question 1197229: rooms 1 2 3 4 5 6 7 8+
47 140 1170 2350 2450 2130 1370 1560 (# of units in thousands)
The table above provides information on housing units in some part of the U.S.
Consider the following five events:
A = the unit has at most four rooms
B = the unit has at least two rooms
C = the unit has between five and seven rooms inclusive
D = the unit has more than seven rooms
E = the unit has less than three rooms
Determine the NUMBER OF OUTCOMES (in thousands) that comprise each event given below.
(a) A or C:
(b) B and C:
(c) not B:
(d) not C:
(e) B and E:
Click here to see answer by math_tutor2020(3816) |
Question 1197244: Find the indicated probability.
In general, the probability that a blood donor has Type A blood is 0.40.
Consider 6 randomly chosen blood donors, what is the probability that exactly half of them have Type A blood?
Click here to see answer by ikleyn(52778) |
Question 1197247: The following statement provides two values. For the pair of values, use a percentage to express their relative change or difference. Use the second given value as the reference value. Also, write a statement describing the result.
The population for a particular region is now 327, 159, 730, and in 1999 it was 274,011,156.
Click here to see answer by math_tutor2020(3816) |
Question 1197262: 3. An aerospace company has submitted bids on two separate government defense contracts, A and B. The company feel it has a 50% chance of winning contract A and a 40% chance of winning contract B. Furthermore, it believes that winning contract A is independent of winning contract B.
a. What is the probability that the company will win both contracts?
b. What is the probability that the company will win either of these contracts?
Click here to see answer by ikleyn(52778) |
Question 1197263: three biased coins C1,C2,C3l ie on the table .Their probabilities of falling heads are 1/3,2/3 and1 respectiely . A coin is picked at random, tossed twice ,and observed to fall heads both times .Calculate the probability that it is C1.
Click here to see answer by ikleyn(52778) |
Question 1197270: The time spent waiting for a tram at an airport follows a uniform distribution on the interval from 0 to 200 seconds.
A tram passenger is randomly selected and their wait time, X, is recorded.
Let p denote the probability that X is at least 10 seconds, and let q denote the probability that X is more than 10 seconds.
(a) Calculate p.
(b) Calculate q.
Click here to see answer by ikleyn(52778) |
Question 1197269: The time spent waiting for a tram at an airport follows a uniform distribution on the interval from 0 to 121 seconds.
Calculate the probability that a randomly selected tram passenger has a wait of more than 10 seconds. Give your answer as a decimal and include four digits after the decimal.
Click here to see answer by ikleyn(52778) |
Question 1197267: The test statistic is z = 2.33, the critical values are z = +/- 1.96. The decision would be to______.
Select one:
a. Support the null hypothesis
b. Support the alternative hypothesis
c. Retain the null hypothesis
d. Reject the null hypothesis
Click here to see answer by ewatrrr(24785) |
Question 1197267: The test statistic is z = 2.33, the critical values are z = +/- 1.96. The decision would be to______.
Select one:
a. Support the null hypothesis
b. Support the alternative hypothesis
c. Retain the null hypothesis
d. Reject the null hypothesis
Click here to see answer by math_tutor2020(3816) |
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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, 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, 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