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

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

Question 1051953: This is known as the Birthday Problem.
(a) Consider a class with 30 students. Compute the probability that at least two of them
have their birthdays on the same day. (For simplicity, ignore the leap year).
(b) How many students should be in class in order to have this probability above 0.5?
Click here to see answer by Edwin McCravy(20054)

Question 1051952: A quiz consists of 6 multiple-choice questions. Each question has 4 possible answers. A
student is unprepared, and he has no choice but guessing answers completely at random.
He passes the quiz if he gets at least 3 questions correctly. What is the probability that he
will pass?
Click here to see answer by Edwin McCravy(20054)

Question 1051994: Three computer viruses arrived as an e-mail attachment. Virus A damages the system
with probability 0.4. Independently of it, virus B damages the system with probability 0.5.
Independently of A and B, virus C damages the system with probability 0.2. What is the
probability that the system gets damaged?
Click here to see answer by stanbon(75887)

Question 1051881: An exam consisted of 20 questions with 5 choices each,where 1 was the correct answer.What is the probability of scoring 80% with random guessing?
Click here to see answer by jorel555(1290)

Question 1052063: This is part c of the following problem. I did the problem and got the correct answer.
A missile guidance system has 5 fail safe components. The probability of each failing is 0.05. Find the probability that all will fail.
ANSWER = (5C5) (0.05)^5 (0.95)^0 = (1) (0.05)^5 (0.95)^0 = 0.0000003125 = 3.125 x 10^-7 = basically equals a zero chance of all 5 failing.
Is it also possible to use the binomial table to get the answer?
Click here to see answer by stanbon(75887)

Question 1052088: A bag of 100 tulip bulbs purchased from a nursery contains 35 red tulip bulbs, 20 yellow tulip bulbs, and 45 purple tulip bulbs. What is the probability that a randomly selected tulip bulb is red?
Click here to see answer by Fombitz(32388)

Question 1052150: how many sets of three can you get from a b c d e f
Click here to see answer by stanbon(75887)

Question 1052174: Shipping line W deals with transportation of goods in containers of various sizes. Charges for each container depend on its weight. A consignment of 800 containers in a particular vessel is in the high seas. Records indicate that the weights are normally distributed. The chances of a container weighing more than 20 tonnes are 97,72% while the chances of a container weighing less than 42,55 tonnes are 99,4%.
(1) Determine the mean � and the standard deviation of the weights of the containers.
(2) Charges of one tonne are �2,50. Determine the number of containers whose weights are more than the mean � but not exceeding 32,2 tonnes. Hence or otherwise, determine the total charges on these containers.
Click here to see answer by stanbon(75887)

Question 1051886: A jury pool consists of 35 people, 13 men and 22 women. Compute the probability that a randomly selected jury of 12 people is all male. (Give your answer as a fraction.)
Click here to see answer by Fombitz(32388)

Question 1052190: In a sample of 300 adults, 120 like chocolate ice cream and 87 like vanilla ice cream. One adult is randomly selected from these adults. Round your answer to 2 decimal places.
a. What is the probability that this adult likes chocolate ice cream?
Probability =
b. What is the probability that this adult likes vanilla ice cream?
Probability =
c. Do these two probabilities add to 1.0?
Click here to see answer by Boreal(15235)

Question 1052231: 53% of all persons in the U.S. population have at least some college education. Choose 10 persons at random. Find the probability that at least 5 do not have any college education.
Thanks!
Click here to see answer by Theo(13342)

Question 1052291: What is the critical value for these? How do I work them out to get the answer?

1. There is an annual hot dog eating contest in Plattsburg, MS and the average number of hot dogs eaten by one person is 36 with a standard deviation of 6. Find the critical value for a person who can eat more than 2 deviations above the mean.
2. Female high school seniors at a particular school have an average height of 65 inches with a standard deviation of 5 inches. Find the critical value for a female high senior who is less than 1 deviation from the mean.
3. The average weight of a newborn at a particular hospital is 96 ounces with a standard deviation of 3 ounces. Find the critical value for a newborn who is 2 standard deviations below the average weight.
4. A company found that 27 out of 150 of its products were defective after retraining its employees. If the company normally has a 40% defective product rate, find the critical value to determine if retraining the employees helped to minimize the number of defective products.
5. A teacher gives 200 students a study guide for a test and the average score was 90 with a standard deviation of 6. She did not give the other 200 students a study guide and their average score was 70 with a standard deviation of 8. Find the critical value to determine whether or not the study guide helped students to increase their test score.

Click here to see answer by ewatrrr(24785)

Question 1052285: Can someone tell me if I worked these problem correctly?
A local zoo has on average 250 visitors per day during its peak season with a standard deviation of 80. Assume that the variable is normally distributed.
1. Find the probability that the zoo will have less than 100 visitors.
z-score = x - mean/standard deviation
z = (100 - 250)/80
z = -1.875
P(X < 100)
P(z < -1.875)
0.0304
2. Find the probability that the zoo will have more than 300 visitors.
z-score = x - mean/standard deviation
z = (300 - 250)/80
z = +0.625
P(X >300)
P(z >0.625)
0.2660
3. Find the probability that the zoo will have between 170 and 320 visitors.
z = (170 - 250)/80 = -1.00
z = (320 - 250)/80 = +0.875
P(170 < X < 320)
P(-1.00 < z < 0.875)
0.6505
4. To be considered as a menu item for Gloria's new restaurant an item must have scored in the top 15% by the food critics in the area. The average item's score is 7 with a standard deviation of 2. Assuming that the variable is normally distributed, find the lowest score possible for a menu item to still be considered.
x = (z)(standard deviation) + mean
1 - .15 = .85
x = (.85)(2) + 7
x = 1.70 + 7
x = 8.70
x = 8.7

5. The average number of absences for a high school senior is 5 days per school year with a standard deviation of 3. Any student whose absences who fall in the upper 10% may be at risk for failure due to absences. How many absences must a senior have to be at risk for failure due to absences? Assume that the distribution is normal and round your answer to the day.
x = (z)(standard deviation) + mean
1 - .10 = .90
x = (.90)(3) + 5
x = 2.70 + 5
x = 7.70
x = 8

6. The faculty at a particular school have attended up to an average 4 years of college with a standard deviation of 2 years. Faculty members who are in the lower 10% of the distribution will be offered the opportunity to obtain additional training. A faculty member must have attended less than ___________ years of school to qualify for the training. Round your answer to the year.
x = (z)(standard deviation) + mean
1 - .10 = .90
x = (.90)(2) + 4
x = 1.80 + 4
x = 5.80
x = 6

7. For a medical study, a researcher will select participants from the middle 30% of the distribution based on hours of sleep per night. If the average number of hours of sleep per night is 6 and the standard deviation is .5 hours, then between which two amounts of hours of sleep will a participant have to get to participate in the study? Round your answers to the nearest tenth.

x = (z)(standard deviation) + mean
1 - .30 = .70
x = (.70)(.5) + 6
x = .350 + 6
x = 6.350
x = 6.4

Click here to see answer by ewatrrr(24785)

Question 1052331: X Y

1 4
6 14
11 24

Covariance can be calculated to be?
correlation coefficient can be calculated to be?
Click here to see answer by Fombitz(32388)

Question 1052388: A DELL computer hardware has a yearly 17% rate of failure. Answer the following question. Round the answer up to six decimals; leave them in decimal form.
What is the probability that, if you buy four (4) computers, none will fail within a year?!
Click here to see answer by ewatrrr(24785)

Question 1052454: 68% of men consider themselves professional baseball fans. You randomly selected 10 men and ask each if he considers himself a professional baseball fan. Find the probability that the number who consider themselves baseball fans is (a) exactly five, (b) at least six, and (c) less than four.
Click here to see answer by ikleyn(52754)

Question 1052489: I tried much in this problem but I didn't get my answer correct.
The question is---
A person draws two cards successively without replacement from a pack of 52 playing cards.He tells that both cards are aces,then the probability that both cards are aces if there are 60% chances that he speaks truth-----

Click here to see answer by Theo(13342)

Question 1052507: Successful implementation of a new system is based on three independent modules. Module
1 works properly with probability 0.96. For modules 2 and 3, these probabilities equal 0.95
and 0.90. Compute the probability that at least one of these three modules fails to work
properly.
Click here to see answer by Fombitz(32388)

Question 1052515: Find the critical value X^2 0.99 associated with a X^2 curve with 10 degrees of freedom.
Click here to see answer by Fombitz(32388)

Question 1052544: Could someone please help me understand this:
How is the mean square computed from the sum of squares?
Thanks for the help!
Click here to see answer by addingup(3677)

Question 1052521: In a certain congressional district, it is known that 20% of the registered voters classify themselves as conservatives. If ten registered voters are selected at random from this district, what is the probability that six of them will be conservatives? (Round your answer to four decimal places.)
Click here to see answer by jorel555(1290)

Question 1052536: Three coins are tossed.
Using H to indicate heads and T to indicate tails, give the following. (To indicate that the first coin is tails, the second coin is tails, and the third coin is heads enter TTH. Enter your answers as a comma-separated list.)
(c) the event F that at least two are heads
Give the following. (Enter the probabilities as fractions.)
(f) p(F)
(i) o(F)
(j) o(G)

Click here to see answer by Fombitz(32388)

Question 1052550: Please check if my answer is right for this.
Find the least squares regression line of the data below using the regression feature of a graphing utility. Then, find the average lengths of cellular calls for the year 2013.
Number Chart: https://s15.postimg.org/3la5pgvcr/graph_gain.png
A.) minutes
B.) minutes -- my answer
C.) minutes
D.) minutes
Click here to see answer by Fombitz(32388)

Question 1052583: The results of a national survey showed that on average, adults sleep 6.6 hours per night. Suppose the standard deviation is 1.4 hours.

a. Use the Tchebyshev's theorem to calculate the percentage of individuals who sleep between 3.8 and 9.4 hours.
c. Assume that the number of hours of sleep follows a bell-shaped distributions. Use the
empirical rule to calculate the percentage of individuals who sleep between 3.8 and 9.4 hours per day. How does the result compare to the value that you obtained using Tchebyshev's theorem in part (a)?

Click here to see answer by Boreal(15235)

Question 1052579: The airline industry defines an on-time flight as one that arrives within 15 minutes of its scheduled time. The following table shows the number of on-time and late flights leaving Philadelphia and arriving in Orlando between November 1 and December 31, 2009, by airlines:

Airlines On-Time Late

Southwest 259 73
US Airways 287 129
Air Trans 182 80

a. What is the probability that a randomly selected flight was Southwest and was on-time?

Click here to see answer by Boreal(15235)

Question 1052581: Compute the standard deviation and variance of two student's quiz grades. Which student has performed more consistently?
Student A quiz grades: 8,7,5,6,19
Student B: 2,3,13,5,6
Click here to see answer by Boreal(15235)

Question 74581: Given a normal distribution with � = 100 and σ = 10, if you select a sample of n = 25, what is the probability that X bar is
a. less than 95?
b. Between 95 amd 97.5?
c. Above 102.2?
d. There is a 65% chance that X bar is above what value?

Click here to see answer by sbepk4(1)

Question 1052622: A card is drawn at random from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a spade?
Click here to see answer by Fombitz(32388)

Question 1052621: A number cube labeled with numbers 1,2,3,4,5 and 6 is tossed. What are the odds in favor of the cube showing a number less than 3?
Click here to see answer by Fombitz(32388)

Question 1052620: How many odd three-digit numbers can be written using digits from the set {2,3,4,5,6} if no digit may be used more than once?
Click here to see answer by Fombitz(32388)

Question 1052525: Approximately 10.3% of American high school students drop out of school before graduation. Choose 10 students entering high school at random. Find the probability that at least 6 graduate.
Thanks
Click here to see answer by Fombitz(32388)

Question 1052606: Find the z value such that 94% of the standard normal curve lies between -z and z. (Round your answer to two decimal places.)
Click here to see answer by Fombitz(32388)

Question 1052600: could you please help me solve this question?
The probability that a married couple pays for their honeymoon is 0.56. You randomly select 5 couples and ask each if they paid for their honeymoon themselves. Find the probability that exactly 4 of the couples said that they paid for their honeymoon.
Click here to see answer by rothauserc(4718)

Question 1052626: Birth weights are normally distributed with a mean of 3421g and a standard deviation of 494 g. If a hospital plans to set up special observation conditions for the lightest 2%
of babies, what weight is used for thecut-off separating the lightest 2%
from the others?
The cut-off weight that separates the lightest 2% of babies from the others is g.

Click here to see answer by ewatrrr(24785)

Question 1052690: You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black
Click here to see answer by jorel555(1290)

Question 1052693: According to Statistics Canada (Share of Non-Alcoholic Beverage Market, 2008), 16% of
Canadians consume coffee, 12% - tea, 72% - others. Twenty five people have registered for
a workshop on potential health hazards associated with consumption of caffeine in food
and dietary supplements.
a) Find the probability that exactly five people from the list of participants prefer drinking
either tea or coffee. Calculate the probability manually and check your answer using Excel.
b) Find the probability that at least two people out of 25 prefer drinking coffee. Calculate
your answer manually and check your answer using Excel.
c) What is the average number of people who prefer tea or coffee?
Click here to see answer by stanbon(75887)

Question 1052705: Tickets for a raffle cost$14. There were 834 tickets sold. One ticket will be randomly selected as the winner, and that person wins $1200 and also the person is given back the cost of the ticket. For someone who buys a ticket, what is the Expected Value (the mean of the distribution)?
If the Expected Value is negative, be sure to include the "-" sign with the answer. Express the answer rounded to two decimal places
Click here to see answer by stanbon(75887)

Question 1052688: Suppose one card is selected at random from an ordinary deck of 52 playing cards. Let A = event a queen is selected and B= event a diamond is selected. Determine P(B|A)
Click here to see answer by ewatrrr(24785)

Question 1052596: Twenty percent of full-time students drop out of a university if a random sample of 6 students is taken what is the probability that. A. no more than 2 students will drop out of school? B. Three students will drop out of school? C. No students will drop out of school? D. All students will drop out of school? E. what are mean and standard deviation of number of students from sample that will drop out of school?
Would you use the binompdf function?
Click here to see answer by ewatrrr(24785)

Question 1052727: mr. meyers is creating a seating chart for his class. There are 12 desks for 9 students. If he creates a different seating chart for every day, how many days will pass until he has to repeat a seating chart?
Click here to see answer by KMST(5328)

Question 1052805: t is known that the average weight of a piece of easter candy is 65.2 grams with a standard deviation of 4 grams. assume distribution is normal.
B.) The study guide wants me to find the probability that the average weight of 50 pieces is between 64 and 66 grams.
Click here to see answer by Theo(13342)

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, 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