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

Question 1171768: A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time is less than 8.9 hours.
Click here to see answer by Boreal(15235)

Question 1172199: In the new Epiphyte Engineering factory 5000 light bulbs Type A are installed. Their lengths of life are normally distributed with a mean of 360 days and a standard deviation of 60 days.
a) If it is decided to replace all bulbs at one specified time, what interval must be allowed between replacements if not more than 10% of bulbs should fail before replacement?
b) What practical considerations might dictate such a replacement policy?
c) The supplier offers a new type of bulb, Type B, that has a mean life of 450 days and the same standard deviation (60 days) as the present type. If these bulbs were to be used how would the replacement time be affected?
d) Determine whether the new type of bulb is preferable given that is costs 25% more than the existing Type A. Present and explain your conclusions.
f) A rival supplier now offers a third type of bulb, Type C, that has a mean life of 432 days and a standard deviation of 45 days. If these bulbs were to be used how would the replacement time be affected?
How should the Type C bulb compare for costs if it is to be adopted? Present and explain your conclusion.

Click here to see answer by Boreal(15235)

Question 1172146: The chart shows the number of accidents for each of the transportation systems in Ghana in 2019.
Transport system Number of accidents
STC - 4520
Bolt - 5100
Yangon - 6850
Uber - 7144
Metro mass - 9950
Use it to answer the following questions;
a) What are the variables under study?
b) Categorize each variable as quantitative or qualitative.
c) Categorize each quantitative variable as discrete or continuous.
d) Identify the level of measurement for each variable.
e) What factors other than safety do you think can influence a person’s choice of transportation system?
Click here to see answer by Boreal(15235)

Question 1171891: Many U.S. households still do not have Internet access. Suppose 25 out of 80 households in a small southern town do not have Internet access. A company that provides high-speed Internet has recently entered the market. As part of the marketing campaign, the company decides to randomly select ten households and offer them red laptops along with a brochure that describes their services. The aim is to build goodwill and, with a free laptop, tempt nonusers into getting Internet access.
a. What is the probability that six laptop recipients do not have Internet access?
(2 Marks)
b. What is the probability that at least five recipients do not have Internet access?
(2 Marks)
c. What is the probability that two or fewer laptop recipients do not have Internet access?
(2 Marks)
d. What is the expected number of laptop recipients who do not have Internet access?
(1 Marks)
e. Calculate the expected value, the variance, and the standard deviation for the recipients who do not have Internet access.

Click here to see answer by Boreal(15235)

Question 1172247: Dear tutor, Please help me solving these problems
1) An unbiased die is tossed. Find the probability that the number obtained is:
(a) An event number (b) Less than 4 (c) Greater than 6
2) A card is randomly drawn from a standard deck of 52 playing cards. Find the probability that the card drawn is:
(a) A king (b) A diamond (c) Not a diamond (d) A king of diamonds
3) A letter is randomly chosen from the word NATIONAL. What is the probability that it will be?
(a) The letter A (b) A vowel (c) The letter S
4) A box contains 3 red discs, 4 green discs, and 5 blue discs. One disc is randomly drawn from the box. What is probability that will be:
(a) red disc (b) A green disc (c) A red disc or green disc (d) Not a blue disc

Click here to see answer by math_tutor2020(3816)

Question 1172241: study was conducted to investigate the effectiveness of bicycle safety helmets in preventing
head injury. The data consist of a random sample of 793 persons who were involved in bicycle
accidents during an one‐year period (Table 1).
Table 1: Head Injury data
Head injury Wearing helmet - Yes Wearing helmet - No
Yes 17 218
No 130 428
a. Compute and compare the proportions of head injury for the group with helmets
versus the group without helmets. What would be your conclusion?
b. Use appropriate statistical techniques to support your conclusion.
Click here to see answer by Theo(13342)

Question 1172248: The weights in pounds of 100 children from various day‐care centre selected randomly given in
worksheet - weight.
c. Draw an appropriate graph to represent the data.
d. Do you think about the distribution of weights? Calculate 95% confidence
interval for mean weight.
e. Calculate the measure of central tendency and dispersion and conclude.
Click here to see answer by ikleyn(52778)

Question 1172262: There are dozens of personality tests available on the World Wide Web. One test, scored on a scale of 0 to 200 , is designed to give an indication of how "personable" the test taker is, with higher scores indicating more "personability."
Suppose that scores on this test have a mean of 110 and a standard deviation of 21 . Complete the following statements about the distribution of scores on this personality test.
According to Chebyshev's theorem, at least
36%,56%,75%,84%,89%
of the scores lie between 68 and 152 .

Click here to see answer by Boreal(15235)

Question 1172258: In big city the average number of rats per quarter block is 6. Assuming that the occurrence of number of rats follows passion distribution. Find out the probability that in randomly selected quarter block.
a)There are exactly 6 rats.
b)There are 6 to 8 rats
c)There are more than 6 rats
d) There are less than 6 rats
Click here to see answer by Boreal(15235)

Question 1172257: Suppose the average length of stay in a chronic disease hospital of a certain type of patient is 80 days with a standard deviation of 20. If it is reasonable to assume an approximately normal distribution of lengths of stay, find the probability that a randomly selected patient from this group will have a length of stay :
(a). Greater than 60 days
(b) Less than 40 days
(c) Between 35 and 55 days
(d) Greater than 100 days
(e) And draw their both normal distribution curve and standard normal distribution
Click here to see answer by Boreal(15235)

Question 1172254: In a village, there are 64 families each of them has four children. Find the probability that each r number of families has exactly two girls
Click here to see answer by Boreal(15235)

Question 1172259: . The number of patients per month referred to an oncologist. The researchers use a rate of 14 patients per month that are referred to the oncologist. What is the probability of
(a) Exactly 9 patients are referred to an oncologist
(b) Between 4 and 13 inclusive are referred to an oncologist
(c) More than 9 are referred to an oncologist
(d) Less than seven are referred to an oncologist
(e) Less than 11, but more than seven are referred to an oncologist
Click here to see answer by ikleyn(52778)

Question 1171872: A person selects a card from a deck. If it is a red card, he wins $1. If it is a black card between or including 2 and 10, he wins $5. if it is a black face card, he wins $10; and if it is a black ace, he wins $100. It costs $5 to play. What is the expectation of the game?
Click here to see answer by VFBundy(438)

Question 1172320: Two cards are drawn from a well shuffled deck of 52 playing cards
1) find the probability that they are both pictured
A) if cards are drawn with replacement
B) if cards are drawn without replacement
2) find the probability of three consecutive 2's turning up in rolling a fair die three times
Click here to see answer by Boreal(15235)

Question 1171724: Suppose you have selected a random sample of n = 11 measurements from a normal distribution. Compare the standard normal z values with the corresponding t values if you were forming the following confidence intervals.
(a) \ 98% confidence interval
z =
t =
(b) \ 95% confidence interval
z =
t =
(c) \ 80% confidence interval
z =
t =

Click here to see answer by Boreal(15235)

Question 1172251: The weights in pounds of 100 children from various day‐care centre selected randomly given in
worksheet - weight.
c. Draw an appropriate graph to represent the data.
d. Do you think about the distribution of weights? Calculate 95% confidence
interval for mean weight.
e. Calculate the measure of central tendency and dispersion and conclude.

Click here to see answer by Boreal(15235)

Question 1172250: A study was conducted to investigate whether oat bran cereal helps to lower serum cholesterol
in men with high cholesterol levels. Fourteen men were randomly placed on a diet which
included either oat bran or cornflakes; after two weeks their low‐density lipoprotein (LDL)
cholesterol levels were recorded. Each man was then switched to the alternative diet. After a
second two‐week period, the LDL cholesterol level of each person was recorded again
(Worksheet Flake). Test to compare the means of LDL cholesterol level. Name the test and state
clearly your null and alternative hypotheses and choice of test size.
Click here to see answer by ikleyn(52778)

Question 1172325: Determine the probability of rolling a sum of 7 on first toss of two number cubes and a sum of 4 on the second toss. (1/72)
Click here to see answer by Boreal(15235)

Question 1172322: A die is thrown and a card is drown from well shuffled deck of 52 playing card at the same time , what is the probability of that an out come consist of
A) even number from the die and diamond from the card
B) a2 from the die and a pictured card from playing card
C) a prime number from the die and a king from the card
D) a composite number from the die and a red card from the playing card
Click here to see answer by Boreal(15235)

Question 1172329: Find the probability of three consecutive 2's turning up in rolling a fair die three times
Click here to see answer by ikleyn(52778)

Question 1172335: A final year student after being interviewed at two companies, he assesses that his probability of getting an offer from company A is 0.8 and the probability that he gets offer from company B is 0.6. If, on the other hand he believes that the probability that he will get offers from both companies is 0.5. Obtain the probability that he will get
(i). at least one offer from these two companies
(ii). offer from neither company
(iii). offer from company A only
Click here to see answer by ikleyn(52778)

Question 1172328: An urn contans 8 balls from number 1 to 8. Four ball are drawn random and without replacement. Let A be the event that exactly two even numbere balls are drawn and they occur on even numbered drawns from the urn. What is probability of event A.
Click here to see answer by Boreal(15235)

Question 1172326: In a sample of 400 burners there were 12 whose internal diameters were not within tolerance
Is this sufficient evidence for concluding that the manufacturing process is turning out more than
2 % defective burners. Take los to be 5%.
Click here to see answer by Boreal(15235)

Question 1172327: An urn contans 8 balls from number 1 to 8. Four ball are drawn random and without replacement. Let A be the event that exactly two odd numbere balls are drawn and they occur on odd number drawns from the urn. What is probability of event A.
Click here to see answer by greenestamps(13200)

Question 1172346: To qualify for a police academy, applicants are given a test of physical ﬁtness. The scores are normally distributed with a mean of 64 and a standard deviation of 9. If only the top 20% of the applicants are selected, ﬁnd the cutoff score.

Click here to see answer by Theo(13342)

Question 1172340: Determine the number of possible 7-digit telephone Nos. if none f the first three digits
(from left) can equal to zero and: (Solve each part separately) [4-Marks]
a) Any digits can be used for the remaining numbers.
b) The first digit must be odd, alternating thereafter between even and odd digits.
c) All digits must be even.
d) No digits can be repeated
Click here to see answer by Boreal(15235)

Question 1172350: Two number cubes are tossed. Find the probability that the numbers showing on the cubes match given that their sum is greater that five? (2/13)
Click here to see answer by math_helper(2461)

Question 1172360: To test the effectiveness of a new vaccine, researchers gave 100 volunteers the conventional treatment
and gave 100 other volunteers the new vaccine. The results are shown in the table below.
===============================================================
|| Treatment || Disease Prevented || Disease Not Prevented ||
==============================================================
||New Vaccine || 68 || 32 ||
==============================================================
||Conventional Treatment || 62 || 38 ||
=============================================================
a. What is the probability that the disease is prevented in a volunteer chosen at random? 13/20
b. What is the probability that the disease is prevented in a volunteer who was given the new vaccine? 17/25
c. What is the probability that the disease is prevented in a volunteer who was not given the new vaccine? 31/50

Click here to see answer by ikleyn(52778)

Question 1172371: What is the graph of function f(x) = Sin(x) + ln(x) - arcTan(5x + 2) in the domain (0, 10)?
[Here arcTan means Inverse of Tan]
Click here to see answer by ikleyn(52778)

Question 1172368: One bag contains 4 white balls and 3 black balls, and a second bag contains 3 white
balls and 5 black balls. One ball is drawn from the first bag and placed unseen in
the second bag. What is the probability that a ball now drawn from the second
bag is black?
Click here to see answer by greenestamps(13200)

Question 1171892: Suppose that the annual household income in a small Midwestern community is normally distributed with a mean of $55,000 and a standard deviation of $4,500.
a. What is the probability that a randomly selected household will have an income between $50,000 and $65,000? (2 Marks)
b. What is the probability that a randomly selected household will have an income of more than $70,000? (2 Marks)
c. What minimum income does a household need to earn to be in the top 5% of incomes?
(2 Marks)
d. What maximum income does a household need to earn to be in the bottom 40% of incomes? (2 Marks)

Click here to see answer by Theo(13342)

Question 1172382: Two boys and two girls are lined up at random. what is the probability that the girls are separated if a girl is at an end?
Click here to see answer by Edwin McCravy(20054)

Question 1172383: Two game tiles, numbered 1 through 9, are selected at random from a box without replacement. If their sum is even, what is the probability that both numbers are odd?
Click here to see answer by ikleyn(52778)

Question 1172385: Using only 0 , 1 , 2 , 3 ,4 how many three digit
(a) even number can be formed (with no repetition ) ?
(b) odd number can be formed (with no repetition) ?
Click here to see answer by Edwin McCravy(20054)

Question 1172381: A bag contains 4 red chips and 4 blue chips. Another bag contains 2 red chips and 6 blue chips. A chip is randomly selected from one of the bags, and found to be blue. What is the probability that the chip is from the first bag?
Click here to see answer by math_tutor2020(3816)

Question 1172380: Two coins are tossed. what is the probability that the one coins shows heads if it is known that at least one coin is tails?
Click here to see answer by math_tutor2020(3816)

Question 1171701: Two independent samples of observations were collected. For the first sample of 60 elements, the mean was 86 and the standard deviation 6. The second sample of 75 elements had a mean of 82 and a standard deviation of 9.
(a) Compute the estimated standard error of the difference between the two means.
(b) Using £ = 0.01, test whether the two sample can reasonably be considered to have come from populations with the same mean.

Click here to see answer by Boreal(15235)

Question 1172413: A study of two doctors finds that the probability of one doctor correctly diagnosing a medical condition is 93/1000 and the probability the second doctor will correctly diagnose a medical condition is 97/100. What is the probability that at least one of the doctors will make a correct diagnosis? "9979/10,000" why is the answer.
Click here to see answer by math_helper(2461)

Question 1172421: Table below are listed the numbers of doctors in various specialties by gender.
Pathology Pediatrics Psychiatry
Male 12575 33020 27803
Female 5604 33351 12292
Choose one doctor at random and find:
(c) Are the characteristics “female” and “pathologist” independent? Explain clearly

Click here to see answer by ikleyn(52778)

Question 1172388: Find how many numbers in the range 1 - 300 are divisible by at least one of the integers 4, 6 and 15 by using inclusion-exclusion principle.
Click here to see answer by ikleyn(52778)

Question 1172393: If A and B are two events such that P(A) = 0.7 and P(B) = 0.5 and P((A u B)') = 0.1. Find P(A\B). [Note Here (A u B)' means complement of A union B]
Click here to see answer by ikleyn(52778)

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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