Tutors Answer Your Questions about Probability-and-statistics (FREE)
Question 667861: Two marbles are drawn without replacement from a jar with 4 black and 3 white marbles. What is the probability that both marbles are white? The the second marble drawn is white, given that the first is black? The the first marble is black and the second marble is white? and at least one of the marbles is black?
Click here to see answer by stanbon(75887)  |
Question 667908: A box contains 7 red balls and 3 black balls. Two balls are drawn. What is the probability of drawing:
(a)a red ball, followed by a black ball, assuming that you replace the first ball before drawing the second?
(b)a black ball on each draw, if the first ball drawn is black (assuming there is no replacement)
Click here to see answer by ewatrrr(24785)  |
Question 667969: A school code consists of two letters followed by 3 digits. The first letter must be K, F, S, T, U, or I. How many codes meet this description? How many codes meet the additional restrictions: no repeated letter, and no digit can be the 0 digit?
Click here to see answer by ewatrrr(24785) |
Question 667998: In testing a new drug, researchers found that 4% of all patients using it will have a mild side effect. A random sample of 13 patients using the drug is selected. Find the probability that exactly two will have this mild side effect.
Click here to see answer by stanbon(75887) |
Question 668447: Assume a system has 5 subsystems. As long as 3 of the subsystems are operational, the system is working. Also assume that each subsystem has a probability of survival equals to 0.9 for 1000 hours of operation without any failure.
What is the probability that the system will survive a 1000 hours of operation without a loss of more than 2 subsystems.
Click here to see answer by stanbon(75887) |
Question 668443: Due to increasing crime rates over the past few years, the Spokane PD wants to implement a new hot spots policing policy. In order to determine which neighborhoods should receive extra patrols, the Chief wants to know which neighborhood has the highest mean number of calls for service per day over the past year. Unfortunately, two neighborhoods have a mean of 18 calls per day. Neighborhood A has an s of 12.23 and Neighborhood B has an s of 7.42. Using a 95% confidence level, calculate confidence intervals for both neighborhoods and then discuss which neighborhood you believe needs the extra patrols and why.
Confused on how to solve without knowing the N. I believe I am thinking about it too much
Click here to see answer by stanbon(75887) |
Question 668477: say there are 5 male undergraduates, 2 female undergrduates, 2 male graduates, and 2 female graduates. find the probability of selecting an undergraduate or a female? i thought it was (7+4)/11 but thats just one ...
Click here to see answer by stanbon(75887) |
Question 668363: Laboratory tests of bacterial counts are often used for declaring a water source "polluted". Suppose that the distribution of bacterial counts in a sample taken from a certain lake is normally distributed with a variance of 9,000,000. Suppose 25 water samples were taken over the course of july 2004 and yielded a mean count of 12,000. Construct an 80% confidence interval estimate of the unknown mean bacterial count in this lake at this time.
Click here to see answer by stanbon(75887) |
Question 668490: In the Following data,
260,164,210,225,244,254,233,184,269,206,158,209,221,213,198,179,214,257,246,221
I got these calculations:
Mean 218.3
Median 217.5
Mode 221
Standard Deviation 31.5
Variance 992.4
Coefficient of Variation 14.43%
Now i ask, which is the best measure of central tendency? Mean, Median, Mode, or does it not matter?
Click here to see answer by lynnlo(4176) |
Question 668364: The manager of the credit department for an oil company would like to determine whether the average monthly balance of credit card holders is higher than Php 3,000. An auditor randomly samples 150 accounts and finds that the average owed is Php 4,170 with a standard deviation of P1,182.50. using the 0.05 level of significance, can the auditor conclude that there is evidence that the average monthly balance is really higher than Php 3,000?
Click here to see answer by stanbon(75887) |
Question 668672: How would you go about solving this problem? I am having difficulty finding an example in my notes.
A multiple-choice test has 7 questions each with 5 responses, one of which is correct. The lowest number of correct answers a student must obtain in order to receive a grade of A is 5. Find the probability of receiving an A by randomly and independently guessing at the correct answer.
Click here to see answer by stanbon(75887) |
Question 668672: How would you go about solving this problem? I am having difficulty finding an example in my notes.
A multiple-choice test has 7 questions each with 5 responses, one of which is correct. The lowest number of correct answers a student must obtain in order to receive a grade of A is 5. Find the probability of receiving an A by randomly and independently guessing at the correct answer.
Click here to see answer by swincher4391(1107)  |
Question 668851: A popular flashlight that uses two D-size batteries was selected, and several of the same models were purchased to test the "continuous-use life" of D batteries. As fresh batteries were installed, each flashlight was turned on and the time noted. When the flashlight no longer produced light, the time was again noted. The resulting "life" data from Rayovac batteries had a mean of 20.3 hours. Assume these values have a normal distribution with a standard deviation of 2.32 hours. (Give your answers correct to four decimal places.)
(a) What is the probability that one randomly selected Rayovac battery will have a test life between 19.2 and 22.7 hours?
.
(b) What is the probability that a randomly selected sample of 4 Rayovac batteries will have a mean test life between 19.2 and 22.7 hours?
.
(c) What is the probability that a randomly selected sample of 16 Rayovac batteries will have a mean test life between 19.2 and 22.7 hours?
.
(d) What is the probability that a randomly selected sample of 67 Rayovac batteries will have a mean test life between 19.2 and 22.7 hours?
.
(e) Describe the effect that the increase in sample size had on the answers for parts (b) - (d).
As sample size increased, the standard error increased, resulting in higher probabilities.
As sample size increased, the standard error increased, resulting in lower probabilities.
As sample size increased, the standard error decreased, resulting in higher probabilities.
As sample size increased, the standard error decreased, resulting in lower probabilities.
Click here to see answer by lynnlo(4176) |
Question 668965: There are three boxes. Two of the boxes have something special in them, while the third one is empty. You are to select two boxes out of three(you don't know which one is empty). You win if you select the two boxes which have something special in them, and lose otherwise. How do you maximize the probability of winning, and what is that probability.
Click here to see answer by ewatrrr(24785) |
Question 669059: An instructor gives his class a set of 19 problems with the information that the next quiz will consist of a random selection of 9 of them. If a student has figured out how to do 12 of the problems, what is the probability the he or she will answer correctly
(a) all 9 problems?
(b) at least 8 problems?
Thank you for your time.
Click here to see answer by stanbon(75887) |
Question 669065: The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best reate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 16 Southwest flights and observing whether they arrive on time. (a) Find the probability that at least 2 flights arrive late.
Thank you for your time.
Click here to see answer by stanbon(75887) |
Question 669087: Title MPAA Budget Gross Length Rating
8 Mile R 41 117 110 6.7
Alone in the Dark R 20 5 96 2.2
Aviator PG-13 116 103 170 7.6
Big Fish PG-13 70 66 125 8
Bourne Identity PG-13 75 121 119 7.4
Break-Up PG-13 52 116 105 5.8
Charlie's Angels: Full Throttle PG-13 120 101 106 4.8
Collateral R 65 100 120 7.7
Crash R 6.5 55 113 8.3
Daddy Day Care PG 60 104 92 5.7
DaVinci Code PG-13 125 213 149 6.5
Eternal Sunshine of the Spotless Mind R 20 34 108 8.6
From Justin to Kelly PG 5 12 81 1.9
Harry Potter Goblet of Fire PG-13 150 290 157 7.8
Hostel R 4.5 47 94 5.8
House of the Dead R 7 10 90 2
Last Samurai R 100 111 154 7.8
Million Dollar Baby PG-13 30 100 132 8.4
Pirates of the Carribbean (II) PG-13 225 322 150 7.5
Rollerball PG-13 70 19 97 2.7
S.W.A.T. PG-13 80 117 117 6
Secret Window PG-13 40 48 96 6.3
Signs PG-13 70 228 106 7
Silent Hill R 50 47 127 6.6
Son of the Mask PG 74 17 94 2
Spider-Man 2 PG-13 200 373 127 7.8
Star Wars III PG-13 113 380 140 8
Sum of All Fears PG-13 68 118 124 6.4
The Pianist R 35 33 150 8.5
The Village PG-13 72 114 108 6.6
Van Helsing PG-13 160 120 132 5.3
Vanilla Sky R 68 101 136 6.8
Walk the Line PG-13 29 120 136 8.1
War of the Worlds PG-13 132 234 116 6.7
Wedding Crashers R 40 209 119 7.3
1. Which variables can be classified as quantitative? Which variables can be classified as qualitative?
2. What is the level of measurement for gross sales (In millions)
3. Calculate the mean and standard deviation of the Length variable for the 35 movies. (Rounded to two decimal places.) Interpret your results
4.Create a chart of Title vs Length. Paste the chart into the document and discuss what the chart is showing. Are there any outliners? If so, which movie(s)?
5. Create a frequency distribution of the viewer ratings using 5 classes. Your first class should be 0 -2
6. Using the frequency distribution created in problem 5, find the probability of the viewer rating between 6.3 and 8.3
7. Using the average and standard deviation for the Length variable from problems #3, find the probability that the length of the 35 movies is less than 120 minutes. Assuming the distribution is normally distributed. Interpret your results.
8. Using the average and standard deviation for the Length variable from problem #3. Find the length of time, x, that corresponds to a z-score of 1.96. Interpret your results
9. Find a point estimate of the mean, u, for gross sales of the 35 movies
10. Use the variable Gross to construct a 90% and 85% Confidence interval. Which is wider? Why?
Click here to see answer by lynnlo(4176) |
Question 669231: A researcher wants to see if there is a relationship between birth order and personality. A sample of n = 100 people is obtained, all of whom grew up in 3-child families. On the basis of the frequencies shown below, can the researcher conclude that there is a significant difference at the .05 level?
Outgoing - 1st Birth Position (BP) - 13, 2nd BP - 31, 3rd BP - 16
Reserved - 1st Birth Position (BP) - 17, 2nd BP - 19, 3rd BP - 4
Click here to see answer by stanbon(75887) |
Question 669278: The measure position called the midquartile of a data set is found using the formula [Q1 + Q3]/2. Find the midquartile of the given data set.
22 36 47 33 35 40 38 24 32 21 37 42
The midquartile is _______.
Click here to see answer by stanbon(75887) |
Question 669134: In 1995, 70% of all children in the U.S. were living with both parents. If 25 children were selected at random in the U.S., what is the probability that at least 15 of them will be living with both of their parents? Round your answer to 4 decimal places.
Click here to see answer by stanbon(75887) |
Question 669501: Need help in Statistics?
1. What are some specific challenges related to creating a histogram in Microsoft Excel?
2. What ethical issues should you consider when creating a graph of data?
3. A sample of 50 undergraduate students answered the
following survey.
1. What is your gender? Female _____ Male _____
2. What is your age (as of last birthday)? _____
3. What is your height (in inches)? _____
4. What is your current registered class designation?
Freshman _____ Sophomore _____
Junior _____ Senior _____
5. What is your major area of study?
Accounting _____ Economics/Finance _____
Information Systems _____
International Business _____ Management _____
Marketing/Retailing _____ Other _____
Undecided _____
6. At the present time, do you plan to attend graduate
school? Yes _____ No _____ Not sure _____
7. What is your current cumulative grade point average?
_____
8. What would you expect your starting annual salary (in
$000) to be if you were to seek employment immediately
after obtaining your bachelor’s degree? _____
9. What do you anticipate your salary to be (in $000) after
five years of full-time work experience? _____
10. What is your current employment status?
Full-time _____ Part-time _____ Unemployed _____
11. How many clubs, groups, organizations, or teams are
you currently affiliated with on campus?
12. How satisfied are you with the student advisement services
on campus? _____
Extremely 1 2 3 4 5 6 7
Extremely
unsatisfied Neutral satisfied
13. About how much money did you spend this semester
for textbooks and supplies? _____
a. Which variables in the survey are categorical?
b. Which variables in the survey are numerical?
c. Which variables are discrete numerical variables?
the following is off the excel spreadsheet but it did not copy the headings right
ID Num Gender Age Height Class Major Grad School GPA Expected Salary Annual Salary in 5 Years Employment Status Number of Affiliations Satisfaction Advisement Spending
ID05 m 19 67 so m y 2.75 40 100 pt 1 1 500
ID08 m 21 71 jr m y 3.26 40 60 pt 0 1 500
ID34 m 20 72 so m y 3.85 60 100 pt 1 1 450
ID50 f 20 66 so is n 3.13 45 80 pt 0 2 500
ID01 m 19 69 so mr y 3.19 40 70 un 0 2 550
ID02 m 21 67 sr m un 3.11 50 60 pt 0 2 400
ID19 m 23 70 jr ef un 2.50 50 75 un 0 2 400
ID27 m 21 73 jr m y 2.45 40 65 pt 0 2 450
ID15 f 19 66 so mr y 3.22 40 80 pt 0 3 600
ID22 f 19 67 so m un 3.00 45 65 pt 0 3 600
ID23 f 19 65 so mr y 3.62 40 90 pt 0 3 400
ID24 f 20 63 jr m un 2.60 40 60 pt 1 3 500
ID31 f 19 69 so mr un 2.87 30 50 pt 0 3 700
ID37 f 19 60 fr a un 2.80 55 80 pt 0 3 450
ID38 f 21 66 jr mr un 2.67 40 65 pt 0 3 800
ID41 f 19 65 so ef un 3.43 50 100 pt 0 3 400
ID47 f 22 66 jr mr n 2.76 40 65 pt 0 3 500
ID39 m 20 69 so a un 2.65 45 80 un 0 3 400
ID46 m 21 68 jr m n 2.42 35 60 pt 1 3 450
ID49 m 20 68 so is n 2.61 40 65 pt 1 3 450
ID09 f 20 62 so mr n 3.21 45 65 pt 0 4 350
ID14 f 21 65 jr mr y 2.94 40 60 pt 0 4 600
ID17 f 19 64 fr ib un 3.09 40 65 un 1 4 250
ID26 f 21 65 sr o n 2.38 40 60 pt 2 4 300
ID40 f 20 63 so is n 2.88 50 80 un 1 4 375
ID07 m 20 68 jr ef y 2.93 50 75 un 0 4 500
ID11 m 36 67 so a un 3.77 60 120 pt 1 4 200
ID18 m 20 67 jr mr n 3.72 50 80 pt 2 4 350
ID20 m 20 70 so ef y 2.74 60 75 un 0 4 400
ID30 m 24 62 so a n 3.33 55 85 pt 0 4 400
ID43 m 20 68 so a un 2.91 45 90 pt 1 4 350
ID45 m 22 69 jr is y 3.62 55 85 un 2 4 400
ID48 m 19 69 fr un un 3.10 45 70 pt 0 4 400
ID12 f 19 65 so a un 3.71 40 60 un 0 5 550
ID13 f 20 65 jr a un 3.20 45 65 pt 3 5 425
ID21 f 20 63 so mr y 3.55 60 100 pt 2 5 500
ID29 f 20 66 so ib un 3.18 50 75 un 1 5 600
ID32 f 33 67 sr a n 3.14 45 75 ft 0 5 500
ID42 f 21 63 jr ef y 3.48 60 110 pt 0 5 500
ID03 m 20 68 jr ef n 3.02 50 60 pt 0 5 450
ID04 m 18 79 fr ef y 4.00 50 57 pt 0 5 360
ID06 m 21 70 jr a y 3.24 60 100 pt 2 5 650
ID16 m 20 69 jr un un 3.34 60 90 pt 0 5 400
ID28 m 30 71 jr m n 3.28 50 75 pt 0 5 550
ID36 m 21 69 so ef n 2.92 55 85 pt 0 5 400
ID44 m 19 72 so a n 2.75 50 80 pt 0 5 525
ID25 f 22 63 sr ef y 3.63 50 150 pt 3 6 1000
ID33 f 19 64 fr ib n 3.44 45 90 pt 1 6 350
ID10 m 19 70 so a y 3.23 50 70 pt 0 6 300
ID35 f 22 61 jr o y 3.50 45 60 un 0 7 600
Click here to see answer by lynnlo(4176) |
Question 669605: The Big Triple at the local racetrack consists of picking the correct order of finish of the first three horses in the ninth race. If there are 12 horses entered in today’s ninth race, how many Big Triple outcomes are possible?
Click here to see answer by ewatrrr(24785) |
Question 669602: BMI in children is approximately normally distributed with a mean of 24.5 and a standard deviation of 6.2. 1) a BMI between 25 and 30 is considered overweight, what proportion of children are overweight? 2) A a BMI of 30 or more is considered obese, what proportion of children are obese? 3) In a random sample of 10 children, what is the probability that their mean BMI exceeds 25?
Click here to see answer by ewatrrr(24785) |
Question 669607: The following are BMI scores measured in 12 patients who are free of diabetes and participating in a study of risk factors for obesity. BMI is measured as the ratio of weight in kilograms to height in meters squared. Generate a 95% confidence interval estimate of the true BMI. 25 27 31 33 26 28 38 41 24 32 35 40
Click here to see answer by ewatrrr(24785) |
Question 669660: There are two defective batteries in one package of six batteries and three defective batteries in the second package of six. If two batteries are selected at random from each package, find the probability that at least three of the four chosen batteries will work.
I know what this is asking for I just can't seem to figure out how to set it up. Thanks for any help I may receive!
Click here to see answer by Theo(13342)  |
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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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