Tutors Answer Your Questions about Probability-and-statistics (FREE)
Question 1160638: The top 10 names for boys in America in the 1880s were John, William, Charles, George, James, Frank, Joseph, Harry, Henry, and Edward. The top 10 names for boys in the 1980s were Michael, Christopher, Matthew, Joshua, David, Daniel, James, John, Robert, and Brian. In how many ways can you choose 5 names from these lists?
Click here to see answer by ikleyn(52754)   |
Question 1160638: The top 10 names for boys in America in the 1880s were John, William, Charles, George, James, Frank, Joseph, Harry, Henry, and Edward. The top 10 names for boys in the 1980s were Michael, Christopher, Matthew, Joshua, David, Daniel, James, John, Robert, and Brian. In how many ways can you choose 5 names from these lists?
Click here to see answer by greenestamps(13195)  |
Question 1160693: Class records at Rockwood College indicate that a student selected at random has probability 0.61 of passing French 101. For the student who passes French 101, the probability is 0.92 that he or she will pass French 102. What is the probability that a student selected at random will pass both French 101 and French 102? (Use 3 decimal places.)
Looking not just for the answer but how to solve.
Click here to see answer by ikleyn(52754) |
Question 1160700: To reduce laboratory costs, water samples from four public swimming pools are combined for one test for the presence of bacteria. Further testing is done only if the combined sample tests positive. Based on past results, there is a 0.008 probability of finding bacteria in a public swimming area. Find the probability that a combined sample from four public swimming areas will reveal the presence of bacteria. Is the probability low enough so that further testing of the individual samples is rarely necessary?
Click here to see answer by Boreal(15235)  |
Question 1160699: A production run is not acceptable for shipment to customers if a sample of 100 items
contains 5% or more defective items. If a production run has a population proportion
defective of P 0.100 , what is the probability that P will be at least 0.05?
(a) In an effort to estimate the mean amount spent per customer for dinner at a major
restaurant, data were collected for a sample of 49 customers over a three-week
period.
(i) Assume a population standard deviation of $10, 000. What is the standard
error of the mean?
(ii) With a .95 probability, what statement can be made about the sampling
error?
(iii) If the sample mean is $90, 400, what is the 95% confidence interval for
population mean?
Click here to see answer by Boreal(15235) |
Question 1160697: At a noodles & company restaurant, the probability that a customer will order a nonalcoholic beverage is .44
Find the probability that in a sample of 8 customers, none of the 8 will order a nonalcoholic beverage. (round to the nearest 4 decimal places)
Find the probability that in a sample of 8 customers, at least 5 will order a nonalcoholic beverage. (round to the nearest 4 decimal places)
Find the probability that in a sample of 8 customers, few than 6 will order a nonalcoholic beverage.(round to the nearest 4 decimal places)
Find the probability that in a sample of 8 customers, all 8 will order a nonalcoholic beverage. (round to the nearest 4 decimal places)
Click here to see answer by Boreal(15235) |
Question 1160659: III. Ten percent of computer parts produced by a certain supplier are defective. A sample of 10 parts was selected randomly. The computer parts produced are independent.
a) What is the probability that the sample contains exactly 3 defective ones?
b) What is the probability that the sample contains at most 2 defective ones?
c) What is the probability that the sample contains at least 3 defective ones?
d) What is the expected number and standard deviation of the defective computer parts produced?
Click here to see answer by Boreal(15235) |
Question 1160719: Use the tree diagram from example 10 in the task. What is the probability that a student will get all the answers wrong?
A. 0
B. 1/2
C. 1/8
D. 1/16
The question and answer choices are in the link here: https://i.imgur.com/2ayzOli.png
Click here to see answer by ikleyn(52754) |
Question 1160722: You pick a card at random.
Card 4, Card 5, and Card 6
What is P(4 or divisor of 28)?
Simplify your answer and write it as a fraction or whole number.
The cards for the question and the question itself are in the question here: https://i.imgur.com/FTe8o9F.png
Click here to see answer by greenestamps(13195) |
Question 1160738: Which of the following is a Hamiltonian Circuit, beginning at vertex A, for the given graph?
A. ADBCA
B. ABCDA
C. ACBDA
D. all of the above
The graph for the question and the question itself are in the question here: https://i.imgur.com/TCEqxzO.png
Click here to see answer by solver91311(24713)  |
Question 1160746: The proportion of adults 25 and older in a certain country with at least a bachelor's
degree is 0,25. Suppose you pick seven adults at random. What is the probability
that exactly three will have a bachelor's degree or higher?
Click here to see answer by ikleyn(52754) |
Question 1160737: Doug is birdwatching at the coast. He records each bird he sees.
What is the experimental probability that the next bird Doug sees will be a cormorant?
Simplify your answer and write it as a fraction or whole number.
P(cormorant) =
The graph for the question and the question itself are in the question here: https://i.imgur.com/n6xVcEY.png
Click here to see answer by MathLover1(20849)  |
Question 1160732: Which of the following is a Hamiltonian Circuit, beginning at vertex A, for the given graph?
A. ADBCA
B. ABCDA
C. ACBDA
D. all of the above
The graph for the question and the question itself are in the question here: https://i.imgur.com/TCEqxzO.png
Click here to see answer by MathLover1(20849) |
Question 1160748: A mathematics professor gives an "extra-credit" (bonus marks) problem on a test. If it
is done correctly, 15 points are added to the test score, and if it is done partially
correctly, 5 points are added; otherwise 5 points are subtracted. Suppose a student's
probability of getting the problem completely right is 1
4
, and only partially correct is 1
2
.
Find the student's mathematical expectation 𝐸 (expected value) for extra credit.
Click here to see answer by ikleyn(52754) |
Question 1160736: The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1800 miles. What is the probability a certain tire of this brand will last between 56,220 miles and 56,760 miles?
0.4920
0.4649
0.9813
0.0180
Click here to see answer by Boreal(15235) |
Question 1160734: According to a particular survey, 14.9% of those who have received a doctor's degree in engineering are blacks.Suppose that 6 people who have received their doctor's degree in engineering are randomly selected, find the probability that at least 2 are black.
Click here to see answer by Boreal(15235) |
Question 1160686: 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 Exactly seven. [Justification required] *
Click here to see answer by Boreal(15235) |
Question 1160758: Compute the inductive probability of the following argument assuming that
epistemic probabilities defer to base rates and chances. (Hint: this is really just
a Bayes’ theorem question.)
1. One in a thousand people have disease X.
2. The chance of a positive test result is 99% for those that have disease X.
3. The chance of a positive test result is 5% for those that don’t have disease
X.
4. Alice just tested positive.
5. Thus, Alice has disease X.
Click here to see answer by Boreal(15235) |
Question 1160792: 1. The following table shows the weight (in kilograms) of 50 sacks of potatoes leaving a
farm shop.
10.41 10.06 9.38 11.36 9.65
11.24 10.58 8.55 10.47 8.22
9.36 9.63 10.33 10.05 11.57
11.36 10.82 8.93 10.08 9.53
10.05 11.30 11.01 9.72 10.67
9.91 10.26 10.67 10.21 8.18
8.70 9.49 10.98 10.01 9.92
9.27 11.69 9.66 9.52 10.40
10.61 8.83 10.11 10.37 9.73
10.72 10.63 12.86 10.62 10.26
Display these data in a stem and leaf plot. Note the number of decimal places and adjust
accordingly. State clearly both the stem and the leaf units.
2. A market researcher asked 650 students what their favourite daily newspaper was. The results are summarised in the frequency table below. Represent these data in an appropriate
graphical manner.
The Times 140
The Sun 200
The Sport 50
The Guardian 120
The Financial Times 20
The Mirror 80
The Daily Mail 10
The Independent 30
3. Produce a histogram for the data on length of mobile phone calls from the exercises in
Chapter 1 (listed again below) and comment on it.
281.4 293.4 306.5 286.6 298.4
312.7 327.7 311.5 314.8 303.3
270.7 293.9 310.9 346.4 304.6
304.1 320.7 283.6 337.5 259.6
305.4 317.9 289.5 286.9 300.5
278.3 300.1 292.6 312.9 302.5
293.2 267.5 326.9 257.7 285.9
299.6 293.9 303.9 323.7 263.5
281.1 306.9 310.2 301.6 313.9
314.8 292.0 302.4 267.9 292.0
Consider the following data for daily sales at a small record shop, before and after a local
radio advertising campaign.
Daily Sales Before After
1000 ≤ sales < 2000 10 7
2000 ≤ sales < 3000 30 10
3000 ≤ sales < 4000 40 25
4000 ≤ sales < 5000 20 35
5000 ≤ sales < 6000 15 37
6000 ≤ sales < 7000 12 40
7000 ≤ sales < 8000 10 20
8000 ≤ sales < 9000 8 10
9000 ≤ sales < 10000 0 5
Totals 145 189
(a) Calculate the percentage relative frequency for before and after.
(b) Calculate the cumulative percentage relative frequency for before and after.
(c) Plot the relative frequency polygons for both on one graph and comment.
(d) Plot the ogives for both on one graph.
(e) Find the level of sales, before and after, that are reached on 25%, 50% and 75% of
days.
Click here to see answer by solver91311(24713) |
Question 1160787: Q.No. 1
A. The amount (in PRs) that the customers deposited at a newly opened branch of national bank are:
12400 1400 15000 28900 5200 15600 20300 8200 2700 24800
3900 5200 10300 5800 13600 24900 11000 29800 25100 15700
18600 10700 14200 18500 7500 20200 11900 21900 15600 7800
11600 15200 20600 11700 5200 29900 5800 15300 21900 14800
14500 18700 16500 14700 15800 14600 18500 18600 14900 14000
a. Develop a box plot of the data values in the data set.
b. Is the data distribution skewed or symmetrical?
c. How many outliers are present in the data?
B. For the box plots below, estimate the values of:
a. the median M
b. the quartiles Q1 and Q3
c. the interquartile range IQR
d. the minimum and maximum values
e. the values of any outliers
Q.No. 2
A. Some people are in favor of reducing federal taxes to increase consumer spending and others are against it. Three persons are selected and their opinions are recorded. Assuming no one is undecided, list the possible outcomes.
B. A sample of 2,000 licensed drivers revealed the following number of speeding violations
a. What is the probability that a particular driver had exactly two speeding violations?
b. What is the probability that a particular driver had three or four violations?
C. What is the probability that a particular driver had three and four violations?
B. Sam is going to assemble a computer by himself. He has the choice of chips from two brands, a hard drive from four, memory from three, and an accessory bundle from five local stores. How many different ways can Sam order the parts?
C. The probability that an American industry will locate in Shanghai, China, is 0.7, the probability it will locate in Beijing, China, is 0.4, and the probability that it will locate in either Shanghai or Beijing or both is 0.8. What is the probability that the industry will locate
a. in both cities?
b. In neither city?
c. E. A random sample of 200 adults are classified below by gender and their level of education attained.
If a person is picked at random from this group, find the probability that
(a) the person is a male, given that the person has a secondary education;
(b) The person does not have a college degree, given that the person is a female.
Q.No. 3
A. A nationwide survey of college seniors by the University of Michigan revealed that almost 70% disapprove of daily pot smoking, according to a report in Parade. If 12 seniors are selected at random and asked their opinion, find the probability that the number who disapprove of smoking pot daily is
(a) Anywhere from 7 to 9;
(b) At most 5;
(c) Not less than 8.
B. The tensile strength of a certain metal component is normally distributed with a mean of 10,000 kilo- grams per square centimeter and a standard deviation of 100 kilograms per square centimeter. Measurements are recorded to the nearest 50 kilograms per square centimeter.
(a) What proportion of these components exceed 10,150 kilograms per square centimeter in tensile strength?
(b) If specifications require that all components have tensile strength between 9800 and 10,200 Kilograms per square centimeter inclusive, what proportion of pieces would we expect to scrap?
Click here to see answer by solver91311(24713) |
Question 1160785: Medical research has concluded that people experience a
common cold roughly two times per year. Assume that the
time between colds is normally distributed with a mean of
160 days and a standard deviation of 40 days.
(a) What is the probability of going 200 or more days between
colds? Of going 365 days?
(b) What is the probability of getting a cold within 80 days of a
previous cold?
Click here to see answer by solver91311(24713) |
Question 1160791: In an experiment, a ball is drawn from an urn containing 14 orange balls and 12 purple balls. If the ball is orange, two coins are tossed. Otherwise, three coins are tossed.
1) How many elements of the sample space will have a orange ball?
2) How many elements of the sample space are there altogether?
Click here to see answer by Edwin McCravy(20054)  |
Question 1160812: A gym knows that each member, on average, spends 50 minutes at the gym per week, with a standard deviation of 10 minutes. Assume the amount of time each customer spends at the gym is normally distributed.
a. Suppose the gym surveys a random sample of 30 members about the amount of time they spend at the gym each week. What are the expected value and standard deviation (standard error) of the sample mean of the time spent at the gym?
b. If 30 members are randomly selected, what is the probability that the average time spent at the gym exceeds 55 minutes?
c. If 30 members are randomly selected, what is the probability that a randomly selected customer spends between 45 minutes to 55 minutes at the gym?
Click here to see answer by Boreal(15235) |
Question 1160795: Two equal groups of seedlings, and equal in height, were selected for an experiment. One group of seedlings was fed Fertilizer A, and the other group with Fertilizer B. The mean heights of the two groups of seedlings, their standard deviations, and sample sizes are listed below. Assume simple random sampling, independence, and normally distributed data. Alpha = 0.025
Sample Mean Height (inches), Std Deviation (inches), Sample Size
Fertilizer A 12.92, 0.25, 15
Fertilizer B 12.63, 0.20, 13
what is the t-statistic rounded off to one decimal place?
Click here to see answer by Boreal(15235) |
Question 1160784: Researchers at Namibia University of Science and Technology (NUST) have determined that
children under 2 years old who sleep with the light on have a 36 % chance of becoming myopic
before they are 16. Children who sleep in darkness have a 21 % chance of becoming myopic. A
survey indicated that 28% of children under 2 sleeps with some light on. Find the probability
that child under 16 is myopic.
Click here to see answer by Boreal(15235) |
Question 1160730: Doug is birdwatching at the coast. He records each bird he sees.
What is the experimental probability that the next bird Doug sees will be a cormorant?
Simplify your answer and write it as a fraction or whole number.
P(cormorant) =
imgu
The graph for the question and the question itself are in the question here: https://i.imgur.com/n6xVcEY.png
Click here to see answer by Boreal(15235) |
Question 1160711: 7. For a random variable that is normally distributed, with mean of 80 and standard deviation of 10, determine the probability that a simple random sample of 25 items will have a mean that is; A. greater than 78. B. between 79 and 85. C. less than 85.
Click here to see answer by Boreal(15235) |
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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, 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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