Tutors Answer Your Questions about Probability-and-statistics (FREE)
Question 1177076: Consider a population consisting of 5 elements: {1,2,3,4,5}. We will draw a sample of size two from this population and calculate the average of drawn numbers. For example, we can get numbers 1 and 5, the average is then 3 or numbers 3 and 4, their average is 3.5. The averages with their probabilities are probability distribution. It is an example of a sampling distribution with sample size 2.
Click here to see answer by greenestamps(13327)   |
Question 1177089: 2.2.4. An experiment has four possible outcomes A, B, C, and D. Check whether the following assignments of probability are possible:
(a) P(A) = 0.20, P(B) = 0.40, P(C) = 0.09, P(D) = 0.31.
(b) P(A) = 0.41, P(B) = 0.17, P(C) = 0.12, P(D) = 0.36.
(c) P(A) = 1/8, P(B) = 1/2, P(C) = 1/4, P(D) = 1/8.
2.2.5. Suppose we toss two coins and suppose that each of the four points in the sample space
S = {(H, H ), (H, T ), (T, H ), (T, T )} is equally likely. Let the events be A = {(H, H ), (H, T )}
and B = {(H, H ), (T, H )}. Find P(A ∪ B).
Click here to see answer by ikleyn(53751)  |
Question 1177092: Suppose we toss two coins and suppose that each of the four points in the sample space
S = {(H, H ), (H, T ), (T, H ), (T, T )} is equally likely. Let the events be A = {(H, H ), (H, T )}
and B = {(H, H ), (T, H )}. Find P(A ∪ B)
Click here to see answer by ikleyn(53751) |
Question 1177092: Suppose we toss two coins and suppose that each of the four points in the sample space
S = {(H, H ), (H, T ), (T, H ), (T, T )} is equally likely. Let the events be A = {(H, H ), (H, T )}
and B = {(H, H ), (T, H )}. Find P(A ∪ B)
Click here to see answer by mccravyedwin(421)  |
Question 1177088: Consider an experiment in which each of three cars exiting from a university main entrance turns right (R) or left (L). Assume that a car will turn right or left with equal probability
of 1/2.
(a) What is the sample space S?
(b) What is the probability that at least one car will turn left?
(c) What is the probability that at most one car will turn left?
(d) What is the probability that exactly two cars will turn left?
(e) What is the probability that all three cars will turn in the same direction?
Click here to see answer by ikleyn(53751) |
Question 1177115: A basketball team won 8 games and lost 7 games. Based on these results: (show all work)
a. What are the odds in favor of winning a basketball game?
b. What is the probability of winning a game, to the nearest hundredth?
c. What are the odds against winning a game?
d. What is the probability of losing a game, to the nearest hundredth?
Click here to see answer by Edwin McCravy(20077)  |
Question 1177120: a. A blue marble is drawn.
b. A red marble is drawn.
c. A red or green marble is drawn.
d. A blue and then a green marble is drawn with replacement.
e. A blue and then a green marble is drawn without replacement.
f. Two green marbles are drawn with replacement.
g. A green marble is drawn.
h. A red or blue marble is drawn.
match these to the above questions!
i. 9/29 x 7/28
ii. 7/29
iii. 13/29
iv. 7/27 x 7/29
v. 9/29 x 7/29
vi. 13/29 + 9/29
vii. 9/29
viii. 13/29 + 7/29
Click here to see answer by ewatrrr(24785)  |
Question 1177120: a. A blue marble is drawn.
b. A red marble is drawn.
c. A red or green marble is drawn.
d. A blue and then a green marble is drawn with replacement.
e. A blue and then a green marble is drawn without replacement.
f. Two green marbles are drawn with replacement.
g. A green marble is drawn.
h. A red or blue marble is drawn.
match these to the above questions!
i. 9/29 x 7/28
ii. 7/29
iii. 13/29
iv. 7/27 x 7/29
v. 9/29 x 7/29
vi. 13/29 + 9/29
vii. 9/29
viii. 13/29 + 7/29
Click here to see answer by greenestamps(13327) |
Question 1177116: State if the following events are independent or dependent. Give a reason
for your answer.
a. Rolling a 5 and then a 3 on a six sided dice.
I think independent because.....
b. Randomly pulling a white sock from a drawer that contains both white and
black socks, not replacing it, and then pulling a black sock from the
drawer.
I think dependent because....
c. Getting a red gumball and then a blue gumball from a gumball machine.
d. Pulling a card from a standard deck of 52 cards, not replacing it, and
then pulling another card from the deck.
e. Pulling a card from a standard deck of 52 cards, replacing it, and then
pulling another card from the deck.
Click here to see answer by Edwin McCravy(20077) |
Question 1177114: A basketball team won 8 games and lost 7 games. Based on these results:(show work)
a. What are the odds in favor of winning a basketball game?
b. What is the probability of winning a game, to the nearest hundredth?
c. What are the odds against winning a game?
d. What is the probability of losing a game, to the nearest hundredth?
Click here to see answer by Boreal(15235)  |
Question 1177121: 12.) Find the P-value for the following values of the test statistic t, statistic t, sample size n, and alternate hypothesis H1. If you use Table A.3, you may specify that P is between two values.
d.)t = 3.635, n = 4, H1: μ > μ0
Table A.3 Critical Values for the Student’s t Distribution
Degrees of
Freedom
Area in Right Tail
0.40
0.25
0.10
0.05
0.025
0.01
0.005
0.0025
0.001
0.0005
1
0.325
1.000
3.078
6.314
12.706
31.821
63.657
127.321
318.309
636.619
2
0.289
0.816
1.886
2.920
4.303
6.965
9.925
14.089
22.327
31.599
3
0.277
0.765
1.638
2.353
3.182
4.541
5.841
7.453
10.215
12.924
4
0.271
0.741
1.533
2.132
2.776
3.747
4.604
5.598
7.173
8.610
5
0.267
0.727
1.476
2.015
2.571
3.365
4.032
4.773
5.893
6.869
6
0.265
0.718
1.440
1.943
2.447
3.143
3.707
4.317
5.208
5.959
7
0.263
0.711
1.415
1.895
2.365
2.998
3.499
4.029
4.785
5.408
8
0.262
0.706
1.397
1.860
2.306
2.896
3.355
3.833
4.501
5.041
9
0.261
0.703
1.383
1.833
2.262
2.821
3.250
3.690
4.297
4.781
10
0.260
0.700
1.372
1.812
2.228
2.764
3.169
3.581
4.144
4.587
11
0.260
0.697
1.363
1.796
2.201
2.718
3.106
3.497
4.025
4.437
12
0.259
0.695
1.356
1.782
2.179
2.681
3.055
3.428
3.930
4.318
13
0.259
0.694
1.350
1.771
2.160
2.650
3.012
3.372
3.852
4.221
14
0.258
0.692
1.345
1.761
2.145
2.624
2.977
3.326
3.787
4.140
15
0.258
0.691
1.341
1.753
2.131
2.602
2.947
3.286
3.733
4.073
16
0.258
0.690
1.337
1.746
2.120
2.583
2.921
3.252
3.686
4.015
17
0.257
0.689
1.333
1.740
2.110
2.567
2.898
3.222
3.646
3.965
18
0.257
0.688
1.330
1.734
2.101
2.552
2.878
3.197
3.610
3.922
19
0.257
0.688
1.328
1.729
2.093
2.539
2.861
3.174
3.579
3.883
20
0.257
0.687
1.325
1.725
2.086
2.528
2.845
3.153
3.552
3.850
21
0.257
0.686
1.323
1.721
2.080
2.518
2.831
3.135
3.527
3.819
22
0.256
0.686
1.321
1.717
2.074
2.508
2.819
3.119
3.505
3.792
23
0.256
0.685
1.319
1.714
2.069
2.500
2.807
3.104
3.485
3.768
24
0.256
0.685
1.318
1.711
2.064
2.492
2.797
3.091
3.467
3.745
25
0.256
0.684
1.316
1.708
2.060
2.485
2.787
3.078
3.450
3.725
26
0.256
0.684
1.315
1.706
2.056
2.479
2.779
3.067
3.435
3.707
27
0.256
0.684
1.314
1.703
2.052
2.473
2.771
3.057
3.421
3.690
28
0.256
0.683
1.313
1.701
2.048
2.467
2.763
3.047
3.408
3.674
29
0.256
0.683
1.311
1.699
2.045
2.462
2.756
3.038
3.396
3.659
30
0.256
0.683
1.310
1.697
2.042
2.457
2.750
3.030
3.385
3.646
31
0.256
0.682
1.309
1.696
2.040
2.453
2.744
3.022
3.375
3.633
32
0.255
0.682
1.309
1.694
2.037
2.449
2.738
3.015
3.365
3.622
33
0.255
0.682
1.308
1.692
2.035
2.445
2.733
3.008
3.356
3.611
34
0.255
0.682
1.307
1.691
2.032
2.441
2.728
3.002
3.348
3.601
35
0.255
0.682
1.306
1.690
2.030
2.438
2.724
2.996
3.340
3.591
36
0.255
0.681
1.306
1.688
2.028
2.434
2.719
2.990
3.333
3.582
37
0.255
0.681
1.305
1.687
2.026
2.431
2.715
2.985
3.326
3.574
38
0.255
0.681
1.304
1.686
2.024
2.429
2.712
2.980
3.319
3.566
39
0.255
0.681
1.304
1.685
2.023
2.426
2.708
2.976
3.313
3.558
40
0.255
0.681
1.303
1.684
2.021
2.423
2.704
2.971
3.307
3.551
50
0.255
0.679
1.299
1.676
2.009
2.403
2.678
2.937
3.261
3.496
60
0.254
0.679
1.296
1.671
2.000
2.390
2.660
2.915
3.232
3.460
80
0.254
0.678
1.292
1.664
1.990
2.374
2.639
2.887
3.195
3.416
100
0.254
0.677
1.290
1.660
1.984
2.364
2.626
2.871
3.174
3.390
200
0.254
0.676
1.286
1.653
1.972
2.345
2.601
2.839
3.131
3.340
z
0.253
0.674
1.282
1.645
1.960
2.326
2.576
2.807
3.090
3.291
20%
50%
80%
90%
95%
98%
99%
99.5%
99.8%
99.9%
Confidence Level
Click here to see answer by Boreal(15235) |
Question 1177082: The proportion of eligible voters in the next election who will vote for the incumbent is assumed to be 52.3%. What is the probability that in a random sample of 600 voters, less than 49.8% say they will vote for the incumbent?
Probability =
I got the result 0.1112 but it tells me that it is wrong.
Click here to see answer by ewatrrr(24785) |
Question 1177117: a. The letters T, C and A are placed in a bag. If a student randomly draws the three letters out, what is the probability that they are drawn in order to spell CAT?
b. A student can create a 3 digit computer password from the numbers 0 to 9. If the digits cannot be repeated, what is the probability of someone guessing the correct password?
c. The padlock on a gym locker consists of any 3 numbers from 1 to 60. If the numbers can repeat, what is the probability a student can guess the code on their first try?
d. Daniel, Amy, and Brad are 3 of the 10 finalists in a singing competition. What is the probability that Daniel, Amy, and Brad will place first, second, and third, in any order?
e. Three students are being selected from a class of 10 to be on a special committee. If Tracy, Sydney, and Sam are in the class, what is the probability that they are selected?
f. The letters of the word ALGORITHMS are placed in a bag, and a student draws 3 letters. What is the probability that the letters selected are 1 vowel and 2 consonants?
g. A student is planning a backpacking trip to Europe, where she will visit 7 countries. If there are 10 countries to choose, what is the probability that three of the countries will be France, Germany, and Italy?
h. The coach of a 10 player handball team has to pick 7 players to be in the starting lineup. If Devyn is on the team, what is the probability that he will be on the starting lineup?
match these to the above questions!
i. 3C3/10C3
ii. 3C3*7C4/10C7
iii. 1/10P3
iv. 3C1*7C2/10C3
v. 1/3P3
vi. 1/60^3
vii. 1C1*9C6/10C7
viii. 3P3/10P3
Click here to see answer by ewatrrr(24785) |
Question 1177123: A random sample of 80 voters found that 56 were going to vote for a certain candidate. Find the 90% confidence interval for the population proportion of voters who will vote for that candidate.
Group of answer choices
Click here to see answer by ewatrrr(24785) |
Question 1177124: A standard deck of 52 cards consists of 4 suits (hearts, clubs, diamonds, and spades). If a student deals 3 cards from a standard deck, determine the probability to the nearest hundredth, that at least one card is a heart. Use the method stated below:
a. direct reasoning (2 marks)
b. indirect reasoning (2 marks)
Click here to see answer by ewatrrr(24785) |
Question 1177126: 9. Create and explain your own example of the following:
a. mutually exclusive events (1 mark)
Flip a coin and get heads and tails.
Mutually exclusive events cannot happen at the same time so you can’t get head and tail at the same time. (is this a good example? or should I add more detail?)
b. non-mutually exclusive events (1 mark)
Click here to see answer by MathLover1(20855)  |
Question 1177137: How many different six-place license plates are possible if the first three places and the last
place are to be occupied by letters and the fourth and fifth places are to be occupied by
numbers?
thanks again for helping answer :)
Click here to see answer by greenestamps(13327) |
Question 1177137: How many different six-place license plates are possible if the first three places and the last
place are to be occupied by letters and the fourth and fifth places are to be occupied by
numbers?
thanks again for helping answer :)
Click here to see answer by ikleyn(53751) |
Question 1177136: A game in a state lottery selects four numbers from a set of numbers, {0,1,2,3,4,5,6,7,8,9},
with no number being repeated. How many possible groups of four numbers are possible?
thank you for helping answer.. :)
Click here to see answer by greenestamps(13327) |
Question 1177157: DNA (deoxyribonucleic acid) is made from a sequence of four nucleotides (A, T, G, or C).
Suppose a region of DNA is 40 nucleotides long. How many possible nucleotide sequences
are there in this region of DNA ?
Thank u
Click here to see answer by ikleyn(53751) |
Question 1177178: Adult male heights are normally distributed with a mean of 70 inches and a standard deviation of 3 inches. The average basketball player is 79 inches tall. Using the empirical rule, approximately what percent of the adult male population is taller than the average basketball player?
0.15%
0.30%
49.85%
99.7%
Click here to see answer by ewatrrr(24785) |
Question 1177204: A student taking taking a midterm exam in Ancient History comes to two questions pertaining to a class that he missed, and so he decides to take a random guess on both questions
One of the questions is true/ false and the other is multiple choice with five possible answer
What is the probability of having  answers to both questions?
Click here to see answer by ikleyn(53751) |
Question 1177224: Please help me with this question:
If the probability that a public health nurse will find a client at home is .7, what is the probability (assuming independence) that on two home visits made in a day both clients will be home?
Regards.
Click here to see answer by ikleyn(53751) |
Question 1177224: Please help me with this question:
If the probability that a public health nurse will find a client at home is .7, what is the probability (assuming independence) that on two home visits made in a day both clients will be home?
Regards.
Click here to see answer by ewatrrr(24785) |
Question 1177215: A card is elected at random from an ordinary deck of 52 playing cards. If E is the event
that the selected card is an ace and F is the event that it is a spade, show that E and F are
independent events
Thank You :)
Click here to see answer by ewatrrr(24785) |
Question 1177196: 1. A survey reports its results by stating that standard error of the mean to be is 20. The population standard deviation is 500.
(i). How large is the sample used in this survey?
(ii). What is the probability that the sample mean will be within 25 of the population mean?
2(a). The time it takes a fire department to respond to a request for emergency aid has a mean of 14 minutes with standard deviation of 4 minutes. Suppose we randomly sample 50 emergency requests over a two-month period.
(i). State the sampling distribution of the sample mean, ̅x.
(ii). What is the probability that the sample mean will be 15 minutes or less?
(iii). What role does the Central Limit Theorem play in identifying this distribution?
(b). A population has a mean of 400 and a standard deviation of 50. The probability distribution of the population is unknown. A research study will use a simple random sample of either 10, 20, 35, or 50. items to collect data about the population.
(i). In which of these sample sizes will you be able to use the Normal probability distribution to describe the sampling distribution of the sample mean, ̅x. Explain.
(iii). Determine the standard error of the sampling distribution of ̅x for the instances where the Normal distribution would be appropriate.
(iii). What theorem would you appeal to for the justification of your answers in (i) and (ii). State it.
Click here to see answer by ewatrrr(24785) |
Question 1177230: 1-The length of time a domestic flight must wait between gate departure and takeoff taxi at Miami International Airport is approximately normally distributed with a mean of 20 minutes and a standard deviation of 5 minutes.
a. What is the probability that a plane must wait between 18 and 24 minutes before taxiing for takeoff after leaving the gate?
b. What is the probability a plane must wait between 22 and 30 minutes before taxiing for takeoff after leaving the gate?
c. What is the probability a plane waits more than 12 minutes between gate departure and takeoff taxi?
d. What is the length of time such that only 5% of planes wait this long or longer before gate departure and taxiing down the runway?
Click here to see answer by ewatrrr(24785) |
Question 1177245: The probability that a randomly selected student from a college is a female is
.55 and the probability that a student works for more than 10 hours per
week is .62. If these two events are independent, find the probability that a
randomly selected student is a
a. male and works for more than 10 hours per week
b. female or works for more than 10 hours per week
Click here to see answer by Solver92311(821)  |
Question 1177252: In a Gallup-type poll, 1080 randomly selected adults were surveyed and 28% of them said that they used the Internet for shopping at least a few timesa year. Construct a 99% confidence interval for the true proportion of adults who shop on the Internet at least a few times a year.
Click here to see answer by ewatrrr(24785) |
Question 1177259: The proportion of eligible voters in the next election who will vote for the incumbent is assumed to be 53.5%. What is the probability that in a random sample of 580 voters, less than 49.8% say they will vote for the incumbent?
Probability =
Click here to see answer by ewatrrr(24785) |
Question 1177253: 6.Insurancecompanies are becoming concerned that the increased use of cell phones is resulting in more car crashes, and they are considering implementing higher rates for drivers who use such phones. They want to estimate the proportion of drivers who talk on phone while they are driving to within 3% with 95% confidence. What size of sample should they take?
Click here to see answer by ewatrrr(24785) |
Question 1177246: The Red Cross honors and recognizes its best volunteers from time to time.
One of the Red Cross offices has received 12 nominations for the next group
of 4 volunteers to be recognized. Eight of these 12 nominated volunteers are
females. If the Red Cross office decides to randomly select 4 names out of
these 12 nominated volunteers, find the probability that of these 4
volunteers
a. exactly 3 are females
b. exactly 1 is female
c. at most 1 is female
Click here to see answer by ewatrrr(24785) |
|
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, 51346..51390, 51391..51435, 51436..51480, 51481..51525
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