Tutors Answer Your Questions about Probability-and-statistics (FREE)
Question 1165742: In a lottery game, a player picks 8 numbers from 1 to 48. If 6 of those 8 numbers match those drawn, the player wins third prize. Let's walk through the steps to determine the probability of winning third prize.
In how many ways can 6 winning numbers be chosen from the possible 8 numbers?
In how many ways can 2 non-winning numbers be chosen from the pool of all non-winning numbers?
The number of favorable outcomes would be to multiply the above two answers together, since we want 6 winning numbers and 2 non-winning numbers. What is the number of favorable outcomes?
In how many ways can you pick any 8 numbers from the pool of 48 numbers? This is your total outcomes.
.
What is the probability of winning third prize?
(Round to 5 decimal places.)
Click here to see answer by CPhill(2138)   |
Question 1165713: a) The probability of being a smoker among a group of cases with lung cancer is 0.75. Calculate the probability that in a group of 6 cases, you have atleast 3 smokers.
b) What are the expected value and variance of the number of smokers?
c) The number of babies born in a day at a hospital's maternity wing follows a Poisson distribution with a mean of 4 in a day. Calculate the probability that five babies are born during a particular day in this maternity wing.
Click here to see answer by CPhill(2138) |
Question 1165713: a) The probability of being a smoker among a group of cases with lung cancer is 0.75. Calculate the probability that in a group of 6 cases, you have atleast 3 smokers.
b) What are the expected value and variance of the number of smokers?
c) The number of babies born in a day at a hospital's maternity wing follows a Poisson distribution with a mean of 4 in a day. Calculate the probability that five babies are born during a particular day in this maternity wing.
Click here to see answer by ikleyn(53339)  |
Question 1165702: Compute and interpret the correlation coefficient for the following coded data:
X (height) 15 18 11 19 20 9
Y(weight) 17 21 24 10 25 16
Fit a regression line Y on X and X on Y and coefficient of correlation?
Click here to see answer by CPhill(2138) |
Question 1165681: Suppose you are playing a Texas Hold’em game with three friends, using a standard 52-card deck. At the starting round each player is dealt 2 cards, and at each continuing round each player is dealt an additional card. Each player can be dealt no more than 5 cards in total. Assume the game is fair and no player fold till the final round.
If you have a pair at the initial round, what is the probability for you to get a Full House (three of a kind and a pair)?
Click here to see answer by CPhill(2138) |
Question 1165671: The following are the age (in years) and systolic blood pressure of 20 apparently
healthy adults.
Age (x) B.P (y)
120
128
141
126
134
128
136
132
140
144
128
136
146
124
143
130
124
121
126
123
20
43
63
26
53
31
58
46
58
70
46
53
60
20
63
43
26
19
31
23
REQUIRED
Using a Statistical package of your choice:
(a) Draw a scatter diagram and interpret it. (5 marks)
(b) Calculate the:
(i) Regression line and interpret it. (10 marks)
(ii) Pearsonian correlation coefficient and interpret your answer. (9 marks)
(iii) Coefficient of determination and interpret your answer. (4 marks)
(c) Using your regression line calculated in (i) estimate the systolic blood
pressure for an adult aged 50.
Click here to see answer by CPhill(2138) |
Question 1165670: A survey of 250 adults showed that 100 of they drank alcohol daily. Calculate
standard error for the adult population that drink alcohol daily and also calculate
the error bounds at 95% confidence level. (10 marks)
(b) You randomly sample 500 sexually active individuals and collect information on
their HIV status and History of STDs. Using Chi-square test at the 5%
significance level, is there evidence of a relationship?
HIV
History STDs No Yes Total
No 92 58 150
Yes 70 280 350
Total 162 338 500
Click here to see answer by CPhill(2138) |
Question 1165668: Pregnant women (within month 4) who were being followed-up by a nutritionist had
weights (kg) equal to: 59, 66, 69, 65, 70, 55, 59, 82, 61, 74.
(a) Calculate the:
(i) mean? (4 marks)
(ii) median? (4 marks)
(iii) standard deviation (7 marks)
(b) Calculate the skewness of the distribution of these weights? (3 marks)
(c) Calculate the coefficient of variation
Click here to see answer by CPhill(2138) |
Question 1165662: A random sample of 40 washing machines of a certain brand produced a 95% confidence interval for the mean replacement time of 10.76 to 12.24 years. What is the margin of error of the estimate for the mean of all washing machines of this brand?
Click here to see answer by CPhill(2138) |
Question 1165661: A college statistics professor has office hours from 9:00 am to 10:30 am daily. A random sample of 20 students waiting to see the professor was selected to estimate the mean waiting time for all students. This sample produced a 95% confidence interval of 18.5 to 26.1 minutes. How should the professor interpret this interval?
Click here to see answer by CPhill(2138) |
Question 1165660: For a t-distribution probability density curve with df = 27, find the two t-values that divide the area under the curve into a middle 0.95 area and two outside areas of 0.025 (this is the critical value for a 95% confidence interval based on the t distribution).
Click here to see answer by CPhill(2138) |
Question 1165659: The monthly earnings of a group of recent business school graduates are normally distributed with a standard deviation of 589 dollars. A researcher wants to estimate the mean monthly earnings of all recent graduates from the school. Find the sample size needed to have a confidence level of 95% and a margin of error of 132 dollars.
Click here to see answer by CPhill(2138) |
Question 1165658: A random sample of 30 students was selected from a large group of students taking a certain calculus test. The mean score for the students in the sample was 88. Assume that σ = 7.4. Construct a 99% confidence interval for the mean score, μ, of all students taking the test.
Click here to see answer by CPhill(2138) |
Question 1158727: 1) 6 cars are picked randomly from a garage which has 4 blacks cars and 2 white cars and 4 red cars find the probability of getting at MOST 1 red car.
2)6 cars are picked randomly from a garage which has 4 black cars and 2 white cars and 4 red cars find the probability of getting at LEAST 1 red car
Click here to see answer by ikleyn(53339) |
Question 1165959: 1. A biomedical research company produces 50% of its insulin at a plant in Kansas City, and the remainder is produced at a plant in Jefferson City. Quality control has shown that 1.3% of the insulin produced at the plant in Kansas City is defective, while 0.5% of the insulin produced at the plant in Jefferson City is defective. What is the probability that a randomly chosen unit of insulin came from the plant in Jefferson City given that it is defective?
2.A diagnostic test for disease X correctly identifies the disease 86% of the time. False positives occur 11%. It is estimated that 5.7% of the population suffers from disease X. Suppose the test is applied to a random individual from the population. Compute the following probabilities. (It may help to draw a probability tree.)
The percentage chance that, given a negative result, the person does not have disease X =
%
The percentage chance that, the person will be misclassified =
%
3.A diagnostic test for disease X correctly identifies the disease 89% of the time. False positives occur 13%. It is estimated that 2.99% of the population suffers from disease X. Suppose the test is applied to a random individual from the population. Compute the following probabilities. (It may help to draw a probability tree.)
The percentage chance that the test will be positive =
%
The probability that, given a positive result, the person has disease X =
%
Click here to see answer by ikleyn(53339) |
Question 732016: If two dates are selected at random from the 365 days of the year, use the counting principal to determine the number of possible outcomes if the dates are selected
A)WITH REPLACMENTS
B) WITHOUT REPLACEMENTS
Click here to see answer by ikleyn(53339) |
Question 731989: A person randomly selects one of the six envelopes shown below. Each envelope contains a check that a person gets to keep. Determine the person's expectation if four envelopes contain a $1000 check and two envelopes contain a $5000 check.
Click here to see answer by ikleyn(53339) |
Question 730309: Five evenly matched horses (Applefarm, Bandy, Cash, Deadbeat, and Egglegs) run in a race.
a. In how many ways can the first-, second-, and third-place horses be determined?
b. Find the probability that Deadbeat finishes first and Bandy finishes second in the race.
c. Find the probability that the first-, second-, and third-place horses are Deadbeat, Egglegs, and Cash, in that order.
Thanks!
Click here to see answer by ikleyn(53339) |
Question 730266: let x be the life of a light bulb in hours with the following probabilities:
p(x<=2000)=0.10
p(x>6000)=0.6
what is the probability of the life of the bulb if p(2000
what is the probability of the life of the bulb is >800?
Click here to see answer by ikleyn(53339) |
Question 1165619: A physician claims that joggers' maximal volume oxygen uptake is greater than the average of all adults. A sample of 15 joggers has a mean of 43.6 milliliters per kilogram (ml/kg) and a standard deviation of 6 ml/kg. If the average of all adults is 36.7 ml/kg, is there enough evidence to support the physician's claim at = 0.05?
First, identify the alternative and the null hypotheses.
Second, calculate the critical value and
Next, use the appropriate formula.
Finally, decide whether or not to reject the null hypothesis.
Click here to see answer by amarjeeth123(573) |
Question 1165483: A psychologist records how many words participants recall from a list under threedifferent conditions: large reward for each word recalled, small reward for each word recalled, and no reward.
a. What is the independent variable? _______________
b. What is the dependent variable? _______________
c. What kind of scale is being used
to measure the dependent variable? ______________
Click here to see answer by CPhill(2138) |
Question 1165346: The manager of a computer retails store is concerned that his suppliers have been giving him laptop computers with lower than average quality. His research shows that replacement times for the model laptop of concern are normally distributed with a mean of 4.2 years and a standard deviation of 0.6 years. He then randomly selects records on 38 laptops sold in the past and finds that the mean replacement time is 3.9 years.
Assuming that the laptop replacement times have a mean of 4.2 years and a standard deviation of 0.6 years, find the probability that 38 randomly selected laptops will have a mean replacement time of 3.9 years or less.
P(M < 3.9 years) =
Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Click here to see answer by CPhill(2138) |
Question 1165342: What type of scale is being used for each of the following measurements?
a. Number of arithmetic problems correctly solved _______________
b. Type of phobia _______________
c. Self-esteem, as measured by self-report questionnaire _______________
d. Annual income in dollars _______________
e. Theoretical orientation toward psychotherapy _______________
f. Heart rate in beats per minute _______________
Click here to see answer by CPhill(2138) |
Question 1165293: A lake in foreign country contains two types of fish. Let X be the random variable for the length (in cm) of the Flamboyant Flapper fish. The expected value of X is E(X) = 29 and the variance Var(X) is 7.
Let Y be the random variable for the length (in cm) of the Boring Beluper fish. The expected value of Y is E(Y) = 21 and the variance Var(Y) is 11.
You and your friend go fishing. You catch a Flamboyant Flapper fish and your friend catchs a Boring Beluper. What is the probability that your friend's Boring Flapper is longer than your Flamboyant Flapper? To be able to work this out you need to know the distribution of the random variable (X-Y).
Calculate the expectation (X-Y), E(X-Y), and the standard deviation of (X-Y), SD(X-Y), assuming that X and Y are independent, and enter your answers below. The expected value of (X-Y) is E(X-Y) = ?
Assuming that X and Y are independent, then the standard deviation of (X-Y) is SD(X-Y) = ? (to 1 d.p.)
Click here to see answer by CPhill(2138) |
Question 1165219: Given below are the last four digits of 18 random phone numbers of your local population.
3,143 4,151 9,341 3,430 8,552 4,184
4,045 3,120 8,132 1,660 2,821 9,139
1,328 4,738 8,929 4,280 4,883 3,919
Fill in the frequency table of the final digit of 18 randomly selected phone numbers.
Using the sample mean of the final four digits (9704 would lead to a mean of 5), compute the mean of the sample means. (Round your answer to 2 decimal places.)
Click here to see answer by CPhill(2138) |
Question 1165218: The Quality Control Department employs five technicians during the day shift. Listed below is the number of times each technician instructed the production foreman to shut down the manufacturing process last week.
Technician Shutdowns
Taylor 3
Hurley 1
Gupta 3
Rousche 3
Huang 1
How many different samples of two technicians are possible from this population?
List all possible samples of two observations each and compute the mean of each sample. (Round your answers to 2 decimal places.)
Compare the mean of the sample means with the population mean. (Round your answers to 2 decimal places.)
Click here to see answer by CPhill(2138) |
Question 1165095: . You've calculated a confidence interval for μ and obtained the range (1000, 2100). If your calculation was based on a sample of size of 25, what assumptions did you have to make for this interval to be valid? a) The sampling distribution must be biased with 24 degrees of freedom. b) The underlying population must have an approximately normal distribution. c) The population must have an approximate t distribution. d) The sampling distribution of the sample mean must have a normal distribution.
Click here to see answer by CPhill(2138) |
Question 729597: It has been reported that 15% of all cars on the highway are traveling at speeds in excess of 65 mph. If the speeds of six random automobiles are measured via radar:
a. What is the probability that exactly 3 cars are speeding?
b. what is the probability that at least one car is going over 65 mph
Click here to see answer by ikleyn(53339) |
Question 729296: Could really use some help on a problem, can someone assist?
You play a game where a single die is rolled. If you roll an odd number, you win the amount of dollars the die shows. If you roll an even number, you lose the number showing. Calculate the expected value of the game, and is it fair?
Click here to see answer by ikleyn(53339) |
Question 729650: A Deck of 52 cards with 26 red and 26 black cards. What is the probability that you guess the color correctly by chance?
I really want to understand how to solve the problem so please include steps and/or formula's.
THANKS SO MUCH.
Click here to see answer by ikleyn(53339) |
Question 729645: Three machines A, B and C produce respectively 60%, 30% and 10 % of the total number of items of a factory. The percentage of defectives output of these machines are 2%, 3% and 4%, respectively. If an item is selected at random and is found defective. Find the probability that the selected item was produced by machine C.
Click here to see answer by ikleyn(53339) |
Question 729490: Q.two stores sell a certain product. Store A has 36% of the sales, 2% of which are defective items, and store B has 64% of the sales, 1% of which are defective items. The difference in defective rates is due to different levels of pre-sale checking of the product. A person receives one of this product as a gift. What is the probability it is defective?
Can you explain how to come out with a solution for this type of problem.?
Click here to see answer by ikleyn(53339) |
Question 729475: 1. A prediction equation for starting salaries (in $1,000s) and SAT scores was performed using simple linear regression. In the regression printout shown below, what can be said about the level of significance for the overall model?
Click here to see answer by ikleyn(53339) |
Question 729623: 90% of the people surveyed believe that the speed limilt on the turnpike should increase. A random sample of 15 people were asked if they believe that the speed limit should be increased and the number who agree were recorded
1. find the probability that exactly 7 believe that the speed limit should be increased
Click here to see answer by ikleyn(53339) |
Question 729328: A quality control engineer at a light bulb plant estimates that 1% of the bulbs it sells are defective. If you purchase a package of 3 bulbs, what is the probability that exactly one of them is defective?
Click here to see answer by ikleyn(53339) |
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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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