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

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 Algebra: Probability and statistics Solvers Lessons Answers archive Quiz In Depth

 Question 322562: Initial diagnosis of a patient's illness was potentially flu (f) cold (C) or hay fever (H) with probabilities of .2, .3, and .5 respectively. A lab test was then taken from the patient. past tests on similar patients show show the following conditional probabilities on the test result being positive + neutral (0) or negative (-) p(+/f)= 0.8 p(o/f)=.1 p(-/f)= .1 P(+/c)= 0.2 p(0/c)=.7 p(-/c)=.1 p(+/h)= 0.1 p(o/h)=.3 p(-/h)=.6 Must be solved with bayes theorem tabular Click here to see answer by stanbon(57967)

 Question 322461: A family has three children. Using ordered triples, give the following: a. The sample space. b. The event E that exactly one is a girl. c. The event F that all three are boys. d. p(E) e. o(E) f. p(F) g. o(F) Click here to see answer by Fombitz(13828)

 Question 322597: A letter is randomly selected from the word Mississippi. What is the probability that the letter will be an s? Click here to see answer by jessica43(140)

 Question 322673: A pair of dice is rolled. Find the probabilities of the given events. a. The sum of four. b. The sum of four, given that the sum is odd. c. The roll is doubles, given that the sum is four. Click here to see answer by solver91311(17077)

 Question 322734: Light Bulb Life Span  The life span of a certain type of light bulb is normally distributed with a mean of 5000 hours and a standard deviation of 150 hours. Estimate the probability that this type of light bulb has a life span is between 4850 and 5300 hours. Click here to see answer by stanbon(57967)

 Question 322735: please help! Bags of Flour  The weights of bags of flour are normally distributed, with a mean of 5 pounds (80 ounces) and a standard deviation of 0.5 ounce. Determine an interval of values into which (a) about 95% of the bags of flour will fall and (b) about 68% of the bags of flour will fall. Click here to see answer by stanbon(57967)

 Question 322703: A math test was given; a sample of the scores yielded the following results: 27, 21, 82, 79, 30, 58, 86, 6, 3, 59, 48, 86, 1, 61, 88, 21 Find the range, standard deviation, and variance for the sample scores Click here to see answer by Fombitz(13828)

 Question 322762: alex had 2.5 times as many books as i do you could also say she has 27 more books than i do. how many do i have? thankyou Click here to see answer by solver91311(17077)

 Question 322795: Two jelly beans are selected, one at a time from a bowl containing 10 black, 10 red and 10 green jelly beans. Let x represent the number of black jelly beans selected in 2 draws from the bowl. (A) If this experiment is completed without replacing the jelly beans, explain why x is not a binomial random variable. (B) If this experiment is completed with replacement of the jelly beans, explain why x is a binomial random variable. (Points :4) Click here to see answer by stanbon(57967)

 Question 322761: i bought a big books the book have 100 pages for \$8 while the smaal book have 25 pages for \$2. I paid \$28 and got total of 650 pages. How many of each did i buy? thankyou Click here to see answer by checkley77(12569)

 Question 322845: A graduate statistics course has seven male and three female students. The professor wants to select two students at random to help her conduct a reseach project. What is the probability that the two students chosen a females? Click here to see answer by stanbon(57967)

 Question 322827: This problem tells me to use the variances unequal formula...could you provide it...thank you. Mauricio Cruz, a wine merchant for Cruz's Spirits Emporium, wants to determine if the average price of imported wine is less than the average price of domestic wine. The data obtained is shown in the table below. Imported Wine Domestic Wine X 7.03 9.78 s 2.31 3.62 n 15 16 40. What is the test value? Use a = 0.05. (Use the variances unequal formula) A) 4.53 B) 2.54 C) 2.50 D) 6.97 Click here to see answer by stanbon(57967)

 Question 322846: Students who graduate from law schools must till pass a bar exam before coming layers. Suppose that in a particular jurisdiction the pass rate for first time test takers is 72%. Candidates who fail the first exam may take it again several months later of those who failed their first test ,88% pass their first attempt. Find the probability that a randomly selected law school graduate becomes a lawyer. Assume that candidates cannot take the exam more than twice. Click here to see answer by stanbon(57967)

 Question 322825: Could you provide the steps to performing this problem...the formulas alone would help...thank you. A dietician investigated whether apples washed in hot water or in cold water turned brown at different rates when exposed to air. She took 13 random apples and cut each in half. She washed one half of each apple in hot water and the other half in cold water, and then put both halves out in a tray. Her results (in hours until turning a particular shade of brown) are in the table below. At  = .01, did she see a difference between the two treatments? Hot Water Cold Water Sample mean 5.50 4.85 Sample variance 2.60 2.00 A) No, because the test value 1.09 is inside the range (-3.055, 3.055). B) No, because the test value 0.79 is inside the range (-3.055, 3.055). C) Yes, because the test value 0.79 is inside the range (-3.012, 3.012). D) Yes, because the test value 1.09 is outside the range (-3.012, 3.012). Click here to see answer by stanbon(57967)

 Question 322921: A box contains a total of 50 textbooks, of which 10 are biology books. If you select 2 at random, determine the probability that neither is a biology book. Click here to see answer by Fombitz(13828)

 Question 322927: A box contains ten balls numbered from 1 to 10. If you pick two balls at random, what is the probability that the sum of the numbers on the two balls is even? (a) 1/2 (b) 47/99 (c) 45/99 (d) 4/ 9 (e) 2/10 Click here to see answer by Alan3354(31518)

 Question 322948: The diameters of oranges in a certain orchard are normally distributed with a mean of 7.10 inches and a standard deviation of 0.50 inches. Show all work. (A) What percentage of the oranges in this orchard have diameters less than 6.8 inches? (B) What percentage of the oranges in this orchard are larger than 7.00 inches? (C) A random sample of 100 oranges is gathered and the mean diameter obtained was 7.00. If another sample of 100 is taken, what is the probability that its sample mean will be greater than 7.00 inches? (D) Why is the z-score used in answering (A), (B), and (C)? (E) Why is the formula for z used in (C) different from that used in (A) and (B)? (Points :10) Click here to see answer by stanbon(57967)

 Question 322989: please help...i tried to work the problem with the formula given z=value-mean/standard deviation According to a survey conducted by television advertisers, the average adult American watches an average of 6.98 hours of television per day. The data is normally distributed with a standard devieation of 3.80 hours. Find the probability that a randomly selected person watches more than 8.00 hours of television a day. 8.00-6.98/3.80=6.163...is this correct? Click here to see answer by stanbon(57967)

 Question 322980: I was wondering if I could get a little help with this question. Which of these situations could be analyzed with a one-way analysis of variance? A) The relationship between gender (male or female) and opinion about the death penalty (favor, oppose, uncertain) B) A comparison of four different age groups with regard to mean hours of watching television per day C) The relationship between weight and height for 12-year old girls D) A comparison of four different age groups with regard to proportion that opposes legalization of marijuana Thanks, Dave Click here to see answer by stanbon(57967)

 Question 322995: Insurance companies have determined that US males between the ages of 16 and 24 drive an average of 10,718 miles each year with a standard deviation of 3763 miles. Assume the datea is normally distributed. For a randomly selected male in that age group, find the probability that he drives less than 12,000 miles per year...i have a formula that i used...i'm just confused because some questions say less than...and some say more than...just wanted to ensure i did this correctly: (12000-10718)/3763=.3407 Click here to see answer by stanbon(57967)

 Question 322916: A certain deck of cards contains 2 blue cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both are not blue? Click here to see answer by Fombitz(13828)

 Question 323068: find the indicated area under the standard normal curve. can someone check me and see if these are correct? Between z=0 and 1.28= .40 To the right ofz=2.40= .0081 between z=1.23 and z=1.90= .0806 between z=0 and z=-2.12= -.4829 to the left of z=-0.46=.3227 between z=-1.45 and z=1.87=.8957 Click here to see answer by stanbon(57967)

 Question 323130: Here is the problem...see below for my question... A bond analyst is analyzing the interest rates for equivalent municipal bonds issued by two different states. At  = .05, is there a difference in the interest rates paid by the two states? State A Sample size 80 Mean interest rate (%) 3.7 Sample variance 0.02 State B Sample Size 70 Mean Interest Rate (%) 4.25 Sample Variance 0.03 A) No, because the test value –0.02 is inside the interval (-1.96, 1.96) B) Yes, because the test value 445.79 is outside the interval (-1.96, 1.96) C) Yes, because the test value –21.11 is outside the interval (-1.96, 1.96) D) Yes, because the test value –8.11 is outside the interval (-1.96, 1.96) I used the t-test to figure this and got the answer 810, which does not match any of the answers. Could you please let me know what formula/steps that should be used on this? Click here to see answer by stanbon(57967)

 Question 323168: I am having some difficulty starting to answer the below. Any advice or help is greatly appreciated. An urn contains 4 green, 6 blue and 10 yellow chips. You pay \$5 to draw a chip from the urn. Here are the rules of the game: if you draw a green chip, the dealer returns you your bet and gives you an additional \$5. if you draw a blue chip, the dealer returns you your bet and gives you \$1. if you draw a yellow chip, the dealer keeps your \$5. What is the expected value of this game? Tip: make a table with x-column money to win/lose (+/-) and probability column P(x) that this happens, then calculate Expected Value of x E(x) for this distribution. Click here to see answer by stanbon(57967)

 Question 323129: A sociologist wants to determine if the life expectancy of people in Africa is less than the life expectancy of people in Asia. The data obtained is shown in the table below. Africa (1) Asia (2) X 55.3 65.2 s 8.1 9.3 n 53 42 What is the null hypothesis? Use a = 0.05 . A) H0:μ1 ³ μ 2 B) H0:μ1 = μ 2 C) H0:μ1 £ μ 2 D) H0:μ1 Ή μ 2 I say the answer is B, because I have not seen a single null hypothesis that is anything but =. Is this correct...if not please explain the reasoning. Thank You Click here to see answer by stanbon(57967)

 Question 323186: Many elementary school students in a school district currently have ear infections. A random sample of children in two different schools found that 16 of 42 at one school and 21 of 36 at the other had this infection. At the .05 level of significance, is there sufficient evidence to conclude that a difference exists between the proportion of students who have ear infections at one school and the other? A) No, there is not sufficient information to reject the hypothesis that the proportions of students at the two schools who have ear infections are the same because the test value 1.78 is inside the acceptance region (-1.96,1.96). B) Yes, there is sufficient information to reject the hypothesis that the proportions of students at the two schools who have ear infections are the same because the test value 2.34 is outside the acceptance region (-1.96,1.96). C) Yes, there is sufficient information to reject the hypothesis that the proportions of students at the two schools who have ear infections are the same because the test value 8.76 is outside the acceptance region (-1.96,1.96). D) Yes, there is sufficient information to reject the hypothesis that the proportions of students at the two schools who have ear infections are the same because the test value 15.73 is outside the acceptance region (-1.96,1.96). I used the z-test for comparing two proportions and got the answer -1.76...did I use the correct formula. Click here to see answer by stanbon(57967)

 Question 323128: Many elementary school students in a school district currently have ear infections. A random sample of children in two different schools found that 16 of 42 at one school and 21 of 36 at the other had this infection. At the .05 level of significance, is there sufficient evidence to conclude that a difference exists between the proportion of students who have ear infections at one school and the other? A) No, there is not sufficient information to reject the hypothesis that the proportions of students at the two schools who have ear infections are the same because the test value –1.78 is inside the acceptance region (-1.96,1.96). B) Yes, there is sufficient information to reject the hypothesis that the proportions of students at the two schools who have ear infections are the same because the test value –2.34 is outside the acceptance region (-1.96,1.96). C) Yes, there is sufficient information to reject the hypothesis that the proportions of students at the two schools who have ear infections are the same because the test value –8.76 is outside the acceptance region (-1.96,1.96). D) Yes, there is sufficient information to reject the hypothesis that the proportions of students at the two schools who have ear infections are the same because the test value –15.73 is outside the acceptance region (-1.96,1.96). I used the z-test for comparing two proportions and got the answer -1.76...did I use the correct formula. Click here to see answer by stanbon(57967)

 Question 323218: The formula for the volume of a rectangular box is V = lwh. If the length of a box is 22 inches, the height is 7 inches, and the total volume is 2,310 square inches, find the width of the box. Click here to see answer by checkley77(12569)

 Question 323235: Train A and B are traveling in the same direction on parallel tracks. Train A is traveling 100 miles per hour and train B is traveling at 120 miles per hour. Train A passes the staion at 7:10 Am. If train B passes the same station at 7:22 Am. At what time will train B catch up with train A? Click here to see answer by galactus(183)
 Question 323235: Train A and B are traveling in the same direction on parallel tracks. Train A is traveling 100 miles per hour and train B is traveling at 120 miles per hour. Train A passes the staion at 7:10 Am. If train B passes the same station at 7:22 Am. At what time will train B catch up with train A? Click here to see answer by Edwin McCravy(8999)

 Question 323240: supposed to use Central Limit Theorem to figure out...please help...i have a ti84 calculator..not sure how to get started The average weight of a bag of Hershey's Miniatures is 368 grams with a standard deviation of 38 grams. You buy 20 bags and find the average weight of the 20 bags is 352 grams. A. Assuming the weight listed on the bag is correct, what is the probability of the mean of the sample being less than 352 grams? B. What do you think of Hershey's claim? C. Would it be unusual to have an individual bag weigh less than 352? Click here to see answer by Edwin McCravy(8999)

 Question 323291: can someone tell me if i did this correctly? The mean weights of Santee Cooper catfish are 12.3 pounds. A random sample of 25 catfish is drawn from this population. what is the probability that the mean weight of the sample is less than 11.9 pounds? assume stand dev=1.2 pounds this is what i did...z=(11.9-12.3)/1.2/sqroot25=-.067 Click here to see answer by stanbon(57967)

 Question 323289: assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution.Find the probability of the given range of pounds lost. Click here to see answer by stanbon(57967)

 Question 323324: A certain deck of cards contains 2 blue cards, 2 red cards, 2 yellow cards, and 2 green cards. If two cards are randomly drawn from the deck, what is the probability that they will both are not blue? A. 15/28 B. 1/4 C. 9/16 D. 1/32 E. 1/16 Click here to see answer by Fombitz(13828)

 Question 323286: 1. (10 points) Refer to the Real Estate data , which reports information on homes sold in Venice, Florida, last year. The data is attached in Excel. Let selling price be the dependent variable and size of the home the independent variable. a. Determine the regression equation. b. Estimate the selling price for a home with an area of 2,200 square feet. c. Determine the 95 percent confidence interval and d. the 95 percent prediction interval for the selling price of a home with 2,200 square feet. Data: Price Bedrooms Size Pool Distance Twnship Garage Baths 263.1 4 2300 1 17 5 1 2 182.4 4 2100 0 19 4 0 2 242.1 3 2300 0 12 3 0 2 213.6 2 2200 0 16 2 0 2.5 139.9 2 2100 0 28 1 0 1.5 245.4 2 2100 1 12 1 1 2 327.2 6 2500 0 15 3 1 2 271.8 2 2100 0 9 2 1 2.5 221.1 3 2300 1 18 1 0 1.5 266.6 4 2400 0 13 4 1 2 292.4 4 2100 0 14 3 1 2 209 2 1700 0 8 4 1 1.5 270.8 6 2500 0 7 4 1 2 246.1 4 2100 0 18 3 1 2 194.4 2 2300 0 11 3 0 2 281.3 3 2100 0 16 2 1 2 172.7 4 2200 1 16 3 0 2 207.5 5 2300 1 21 4 0 2.5 198.9 3 2200 1 10 4 1 2 209.3 6 1900 1 15 4 1 2 252.3 4 2600 0 8 4 1 2 192.9 4 1900 1 14 2 1 2.5 209.3 5 2100 0 20 5 0 1.5 345.3 8 2600 0 9 4 1 2 326.3 6 2100 0 11 5 1 3 173.1 2 2200 1 21 5 1 1.5 187 2 1900 0 26 4 0 2 257.2 2 2100 0 9 4 1 2 233 3 2200 0 14 3 1 1.5 180.4 2 2000 0 11 5 0 2 234 2 1700 0 19 3 1 2 207.1 2 2000 0 11 5 1 2 247.7 5 2400 0 16 2 1 2 166.2 3 2000 1 16 2 1 2 177.1 2 1900 0 10 5 1 2 182.7 4 2000 1 14 4 0 2.5 216 4 2300 0 19 2 0 2 312.1 6 2600 0 7 5 1 2.5 199.8 3 2100 0 19 3 1 2 273.2 5 2200 0 16 2 1 3 206 3 2100 1 9 3 0 1.5 232.2 3 1900 1 16 1 1 1.5 198.3 4 2100 1 19 1 1 1.5 205.1 3 2000 1 20 4 0 2 175.6 4 2300 1 24 4 1 2 307.8 3 2400 1 21 2 1 3 269.2 5 2200 0 8 5 1 3 224.8 3 2200 0 17 1 1 2.5 171.6 3 2000 1 16 4 0 2 216.8 3 2200 0 15 1 1 2 192.6 6 2200 1 14 1 0 2 236.4 5 2200 0 20 3 1 2 172.4 3 2200 0 23 3 0 2 251.4 3 1900 0 12 2 1 2 246 6 2300 0 7 3 1 3 147.4 6 1700 1 12 1 0 2 176 4 2200 0 15 1 1 2 228.4 3 2300 0 17 5 1 1.5 166.5 3 1600 1 19 3 0 2.5 189.4 4 2200 0 24 1 1 2 312.1 7 2400 0 13 3 1 3 289.8 6 2000 0 21 3 1 3 269.9 5 2200 1 11 4 1 2.5 154.3 2 2000 0 13 2 0 2 222.1 2 2100 0 9 5 1 2 209.7 5 2200 1 13 2 1 2 190.9 3 2200 1 18 3 1 2 254.3 4 2500 1 15 3 1 2 207.5 3 2100 1 10 2 0 2 209.7 4 2200 1 19 2 1 2 294 2 2100 0 13 2 1 2.5 176.3 2 2000 1 17 3 0 2 294.3 7 2400 0 8 4 1 2 224 3 1900 1 6 1 1 2 125 2 1900 0 18 4 0 1.5 236.8 4 2600 1 17 5 1 2 164.1 4 2300 0 19 4 0 2 217.8 3 2500 0 12 3 0 2 192.2 2 2400 0 16 2 0 2.5 125.9 2 2400 0 28 1 0 1.5 220.9 2 2300 1 12 1 1 2 294.5 6 2700 0 15 3 1 2 244.6 2 2300 0 9 2 1 2.5 199 3 2500 1 18 1 0 1.5 240 4 2600 0 13 4 1 2 263.2 4 2300 0 14 3 1 2 188.1 2 1900 0 8 4 1 1.5 243.7 6 2700 0 7 4 1 2 221.5 4 2300 0 18 3 1 2 175 2 2500 0 11 3 0 2 253.2 3 2300 0 16 2 1 2 155.4 4 2400 1 16 3 0 2 186.7 5 2500 1 21 4 0 2.5 179 3 2400 1 10 4 1 2 188.3 6 2100 1 15 4 1 2 227.1 4 2900 0 8 4 1 2 173.6 4 2100 1 14 2 1 2.5 188.3 5 2300 0 20 5 0 1.5 310.8 8 2900 0 9 4 1 2 293.7 6 2400 0 11 5 1 3 179 3 2400 0 8 4 1 2 188.3 6 2100 1 14 2 1 2.5 227.1 4 2900 0 20 5 0 1.5 173.6 4 2100 0 9 4 1 2 188.3 5 2300 0 11 5 1 3 Click here to see answer by Fombitz(13828)

 Question 323256: can someone tell me if these are correct please..find the indicated z-scores indicated by the graph.. area=0.2776 z=-0.59 area=0.8508 z=1.04 area=.1093 z=-1.23 **not sure how to do this one**area on each end=0.1251=?? Click here to see answer by stanbon(57967)

 Question 323255: Billy Bobs carpet barn is concerned about the delivery times of one of their drivers. The word on the street is that he likes to pull off the side of the road and study statistics when he thinks no one is looking. Billy Bobs has two other drivers. Sample delivery times (in minutes) for each driver follow. At the .05 significance level is there a difference in the mean delivery time? Driver 1 Driver 2 Driver 3 21 29 29 28 26 22 30 25 27 21 26 24 22 27 27 25 22 29 26 21 27 1. State the null and alternate hypothesis. 2. State the decision rule (we reject Ho when). 3. What is the calculated F-statistic 4. What is your decision regarding the null hypothesis? Click here to see answer by stanbon(57967)

 Question 323342: A box contains ten balls numbered from 1 to 10. If you pick two balls at random, what is the probability that the sum of the numbers on the two balls is even? Click here to see answer by galactus(183)
 Question 323342: A box contains ten balls numbered from 1 to 10. If you pick two balls at random, what is the probability that the sum of the numbers on the two balls is even? Click here to see answer by Alan3354(31518)

 Question 323371: If a number is selected at random from the set of all five-digit numbers in which the sum of the digits is equal to 43, compute the probability that this number will be divisible by 11. Click here to see answer by Edwin McCravy(8999)

 Question 323449: find the value of z such that 40% of the distribution lies between it and the mean. Click here to see answer by Edwin McCravy(8999)

 Question 323552: Solve the following equations for the unknown 5x = 20 Click here to see answer by rfer(12730)

 Question 323553: Two dice are rolled and one letter is chosen from a, b or c. Use the counting principle to determine the number of possible outcomes. Click here to see answer by Fombitz(13828)

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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