# 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 138546: The weekly sales (in thousands of dollars) the week before and the week after a new Internet sales location is installed are given in the following table for 8 different businesses. Sales Before Sales After 27 ------------ 32 35 ------------ 36 22 ------------ 23 13 ------------ 12 45 ------------ 48 55 ------------ 57 60 ------------ 58 18 ------------ 30 The alternative hypothesis is HA: d > 0, where d = sales after – sales before. For level of significance 0.10, what is the critical value and the value of the test statistic? a. 1.645 and 1.70 b. 1.70 and 1.645 c. 1.70 and 1.895 d. 1.895 and 1.70 Click here to see answer by stanbon(57303)

 Question 138586: Statistical software is commonly used for problem solving in the workplace. It is useful to look at a computer generated output to understand the format of the output, how the computerized solution treats an ANOVA table, and so on. The ANOVA table is somewhat standardized among various software packages. Formulate the null and alternate hypothesis and decide whether or not to reject it from the ANOVA table data provided below. Group 1 5 7 4 5 4 6 8 5 6 7 Group 2 6 7 7 5 6 7 8 6 8 6 Group 3 7 8 9 8 9 9 10 11 10 9 One factor ANOVA Mean n Std. Dev 7.1 5.7 10 1.34 Group 1 7.1 6.6 10 0.97 Group 2 7.1 9.0 10 1.15 Group 3 7.1 30 1.81 Total ANOVA table Source SS df MS F p-value Treatment 58.20 2 29.100 21.53 2.57E-06 Error 36.50 27 1.352 Total 94.70 29 Post hoc analysis Tukey simultaneous comparison t-values (d.f. = 27) Group 1 Group 2 Group 3 5.7 6.6 9.0 Group 1 5.7 Group 2 6.6 1.73 Group 3 9.0 6.35 4.62 critical values for experimentwise error rate: 0.05 2.49 0.01 3.18 p-values for pairwise t-tests Group 1 Group 2 Group 3 5.7 6.6 9.0 Group 1 5.7 Group 2 6.6 .0949 Group 3 9.0 8.54E-07 .0001 Click here to see answer by stanbon(57303)

 Question 138547: Sherry Weinstein, a buyer, has decided that she will spend an extra \$7 per shirt for the next 10,000 T-shirts she buys for her chain of stores only if the vendor of the more expensive shirt can show conclusive evidence that its shirt can withstand at least 20 more times in the wash without fading. The vendor elected to set 1 as the mean number of washes without fading for the more expensive shirt. An appropriate null hypothesis for the vendor to test is: a. H0: u1 – u2<= 20. b. H0: u1 – u2 < 20. c. H0: u1 – u2 > 20. d. H0: u1 – u2<= 0. Click here to see answer by stanbon(57303)

 Question 138528: In a bumper test, three types of autos were delibertely crashed into a barrier at 5 mph, and the resulting damage(in dollars) was estimated. Five test vehicles of each type were crashed with the results showned below. Research question? Are the mean crash damages the same for these three vehicles? crash 1 Goliath 1,600, 760, 880, 1,950, 1,220 Vermint 1,290, 1,400, 1,390, 1,850, 950 Weasel 1,090, 2,100, 1,830, 1,250, 1,920 Click here to see answer by stanbon(57303)

 Question 138510: The mean science achievement score of a group of Grade 8 students is 78 and s of 10. Granting that the scores of these students are normally distributed, how many would you expect to score less than 85? If the number of students who took the test is 200, how many would that be? How many students would score more than 85? Click here to see answer by stanbon(57303)

 Question 138607: To Stanbon, Using the first problem you solved on z-score please check this problem I tried to solve: The mean weight of 545 women is 99lbs. and s is 5, Assuming that the wts. of women are normally distributed, how many would you expect to weigh less than 105? Z= 105-99/5 z=1.2 from table: Z score = .3848 or 38.48% will weigh more than 105 that is 210 women computing for women who will weigh less than 105: 100-38.48 = 61.52% 545x.6152 = 335 women who will weigh less 105 lbs. Thanks again. Click here to see answer by stanbon(57303)

 Question 138618: In Dallas, some fire trucks were painted yellow (instead of red) to heighten their visibility. During a test period, the fleet of red fire trucks made 153,348 runs and had 20 accidents while the fleet of yellow fire trucks made 135,035 runs and had four accidents. At a=.01, did the yellow fire trucks have a significantly lower accident rate? (a)state the hypothesis, (b) state the decision rule and sketch it. (c)Find the sample porportions and z test statistics. (d) make a decision (e) find the p-value and interpret it. (f) If statistically significant, do you think the difference is large enough to be important? If so, to whom, and why? (g) Is the normanility assumption fulfilled? Explain. Accident Rate for Dallas Fire Trucks Statistic Red Fire Trucks Yellow Fire Trucks Number of accidents x1 =20 accidents x2=4 accidents Number of Fire Runs n1=153,348 Runs n2 = 135,035 Runs Click here to see answer by stanbon(57303)

 Question 138655: If 20 students register for a Sociology class and 35 students register for Psychology, and 15 students register for both classes, if one student is selected at random, what is the probability that student only registered for Sociology or Psychology? Click here to see answer by Edwin McCravy(8906)

 Question 138677: Hello, need some help w/these few. Thanks again, you are awesome! T F 1. An estimate of the population mean based on a large sample is less reliable than an estimate made using a small sample. T F 2. The standard error of the mean will vary according to the size of the sample. As the sample size gets larger, the variability of the sample means gets smaller. T F 3. One misconception about the number to sample is that a larger sample of voters must be selected from a heavily populated state, such as New York, than from a small state such as Nevada. T F 4. If nonprobability sampling methods are used, the results may be biased. T F 5. The Central Limit Theorem states that if all samples of a particular size are selected from any population, the sampling distribution of the sample means is approximately a normal distribution. T F 6. If the size of a sample equals the size of the population, we would not expect any error in estimating the population parameter. Click here to see answer by stanbon(57303)

 Question 138658: An insurance company charges \$200 for a life insurance premium for people under the age of 18 that pays out \$15,000. The probability that someone dies before their 18th birthday is 0.0025. What is the expected payout by the insurance company? How much of that profit/loss does the company make? Click here to see answer by stanbon(57303)

 Question 138647: A regress analysis between sales (Y in \$1000) and advertisting (X in dollars) resulted in the following equation ^Y = 30,000 + 4 X The above equation implies that an A) increase of \$4 in advertising is associated with an increase of \$4,000 in sales. B) increase of \$1 in advertising is associated with an increase of \$4 in sales. C) increase of \$1 in advertising is associated with an increase of \$34,000 in sales. D) increase of \$1 in advertising is associated with an increase of \$4,000 in sales. Click here to see answer by stanbon(57303)

 Question 138699: Please help with this problem. Don't know which text the intructor got it from. Thank you!! A sample of 36 observations is selected from a normal population. The sample mean is 21, and the sample standard deviation is 5. Conduct the following test of hypothesis using the .05 significance level. H0: µ ≥ 20 H1: µ < 20 Answer the Questions: (a) Is this a one or two tailed test? (b) What is the decision rule? (c) What is the value of the test statistic? (d) What is your decision regarding H0? (e) What is the p-value? Interpret it. Click here to see answer by stanbon(57303)

 Question 138728: Sixty-four students in an introductory college economics class were asked how many credits they had earned in college, and how certain there were about their choice of major. Research question: At a=.01, is the degree of certainty independent or credits earned? Row 1 credits earned --Row 2 very uncertain --Row 3 somewhat certain --Row 4 very certain -- Row 5 Row total Credits earned very uncertain somewhat certain very certain Row total 0-9 12 8 3 23 10-59 8 4 10 22 60 or more 1 7 11 19 Col Total 21 19 24 64 Click here to see answer by stanbon(57303)

 Question 136507: I am having problems trying to figure out can you help thanks. In a bumper test, three types of autos were deliberately crashed into a barrier at 5 mph, and the resulting damage (in dollars) was estimated. Five test vehicles of each type were crashed, with the results shown below. Research question: Are the mean crash damages the same for these three vehicles. ```Crash Damage (\$) Goliath Varmint Weasel 1,600 1,290 1,090 760 1,400 2,100 880 1,390 1,830 1,950 1,850 1,250 1,220 950 1,920 ``` Click here to see answer by melissa182(1)

 Question 138738: Why are probabilities number 0 to 1? Why can't the number be greater than 1? Why can't it be negative? Click here to see answer by stanbon(57303)

 Question 138706: Stan, will you please explain how you got the answers below. Thank you very much The ANOVA table is somewhat standardized among various software packages. Formulate the null and alternate hypothesis and decide whether or not to reject it from the ANOVA table data provided below. ------------------------------------------ One factor ANOVA Mean n Std. Dev 7.1 5.7 10 1.34 Group 1 7.1 6.6 10 0.97 Group 2 7.1 9.0 10 1.15 Group 3 7.1 30 1.81 Total ANOVA table Source.. SS df MS F p-value Treatment 58.20 2 29.100 21.53 ...2.57E-06 Error ........36.50 27 1.352 Total ........94.70 29 Post hoc analysis Tukey simultaneous comparison t-values (d.f. = 27) Group 1 Group 2 Group 3 5.7 6.6 9.0 Group 1 ........5.7 Group 2 ........6.6 1.73 Group 3 ........9.0 6.35 4.62 critical values for experimentwise error rate: 0.05 2.49 0.01 3.18 p-values for pairwise t-tests Group 1 Group 2 Group 3 5.7 6.6 9.0 Group 1 ........5.7 Group 2 ........6.6 .0949 Group 3 ........9.0 8.54E-07 .0001 --------------------------------------------------- Ho: The means of the three Groups were all equal Ha: At least one of the means was different. Since p-value = 0.00000257, Reject Ho. Conclusion: At least one of the mean values is different. =============================== Cheers, Stan H. Click here to see answer by stanbon(57303)

 Question 138779: 13.32 An expert witness in a case of alleged racial discrimination in a state university school of nursing introduced a regression of the determinants of Salary of each professor for each year during an 8-year period (n = 423) with the following results, with dependent variable Year (year in which the salary was observed) and predictors YearHire (year when the individual was hired), Race (1 if individual is black, 0 otherwise), and Rank (1 if individual is an assistant professor, 0 otherwise). Interpret these results. Variable Coefficient t p Intercept −3,816,521 −29.4 .000 Year 1,948 29.8 .000 YearHire −826 −5.5 .000 Race −2,093 −4.3 .000 Rank −6,438 −22.3 .000 R2 = 0.811 R2 adj = 0.809 s = 3,318 Click here to see answer by stanbon(57303)

 Question 138790: In a bumper test, three types of autos were deliberately crashed into a barrier at 5 mph, and the resulting damage (in dollars) was estimated. Five test vehicles of each type were crashed, with the results shown below Research question: Are the mean crash damages the same for these three vehicles? Crash1 Applying ANOVA and Nonparametric Tests Simulation Click here to see answer by stanbon(57303)

 Question 138793: In a three-digit lottery, each of the three digits is supposed to have the same probability of occurrence (counting initial blanks as zeros, e.g., 32 is treated as 032). The table shows the frequency of occurrence of each digit for 90 consecutive daily three-digit drawings. Digit Frequency 0 33 1 17 2 25 3 30 4 31 5 28 6 24 7 25 8 32 9 25 Total 270 Perform the chi-square test for a uniform distribution. At α = .05, can you reject the hypothesis that the digits are from a uniform population? Click here to see answer by stanbon(57303)

 Question 138805: 15.28 Can people really identify their favorite brand of cola? Volunteers tasted Coca-Cola Classic, Pepsi, Diet Coke, and Diet Pepsi, with the results shown below. Research question: At α = .05, is the correctness of the prediction different for the two types of cola drinkers? Could you identify your favorite brand in this kind of test? Since it is a 2 × 2 table, try also a two-tailed two-sample z test for π1 = π2 (see Chapter 10) and verify that z2 is the same as your chi-square statistic.Which test do you prefer? Why? Below is the table: Correct? Regular Cola Diet Cola Row Total Yes, got it right 7 7 14 No, got it wrong 12 20 32 Col Total 19 27 46 Click here to see answer by stanbon(57303)

 Question 138787: A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were 3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477 (a) Construct a 90 percent confidence interval for the true mean weight. (b) What sample size would be necessary to estimate the true weight with an error of ± 0.03 grams with 90 percent confidence? (c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture. (Data are from a project by MBA student Henry Scussel.) Click here to see answer by stanbon(57303)

 Question 138698: Please help with this problem. Don't know which text the instructor got it from. Thank you! The following sample observations were randomly selected X: 5 3 6 3 4 4 6 8 Y: 13 15 7 12 13 11 9 5 Determine the coefficient of correlation and the coefficient of determination. Interpret. Click here to see answer by stanbon(57303)

 Question 138778: 13.30 A researcher used stepwise regression to create regression models to predict BirthRate (births per 1,000) using five predictors: LifeExp (life expectancy in years), InfMort (infant mortality rate), Density (population density per square kilometer), GDPCap (Gross Domestic Product per capita), and Literate (literacy percent). Interpret these results. Regression Analysis—Stepwise Selection (best model of each size) 153 observations BirthRate is the dependent variable p-values for the coefficients Nvar LifeExp InfMort Density GDPCap Literate s Adj R2 R2 1 .0000 6.318 .722 .724 2 .0000 .0000 5.334 .802 .805 3 .0000 .0242 .0000 5.261 .807 .811 4 .5764 .0000 .0311 .0000 5.273 .806 .812 5 .5937 .0000 .6289 .0440 .0000 5.287 .805 .812 Click here to see answer by stanbon(57303)

 Question 138784: Please help with this problem. No ISBN available to provide. Thank you!!!! . The following sample observations were randomly selected X: 5 3 6 3 4 4 6 8 Y: 13 15 7 12 13 11 9 5 Determine the coefficient of correlation and the coefficient of determination. Interpret. Click here to see answer by stanbon(57303)

 Question 138776: 12.48 In the following regression, X = weekly pay, Y = income tax withheld, and n = 35 McDonald’s employees. (a) Write the fitted regression equation. (b) State the degrees of freedom for a twotailed test for zero slope, and use Appendix D to find the critical value at α = .05. (c) What is your conclusion about the slope? (d) Interpret the 95 percent confidence limits for the slope. (e) Verify that F = t2 for the slope. (f) In your own words, describe the fit of this regression. R2 0.202 Std. Error 6.816 n 35 ANOVA table Source SS df MS F p-value Regression 387.6959 1 387.6959 8.35 .0068 Residual 1,533.0614 33 46.4564 Total 1,920.7573 34 Regression output confidence interval variables coefficients std. error t (df = 33) p-value 95% lower 95% upper Intercept 30.7963 6.4078 4.806 .0000 17.7595 43.8331 Slope 0.0343 0.0119 2.889 .0068 0.0101 0.0584 Click here to see answer by stanbon(57303)

 Question 138846: need to know how to solve the equation for least square regression line y-hat = b0+b1X b1= [Exiyi - [(Exi*Eyi)/n]] / [E(xi^2) - [(Exi)^2]/n] bo = y-bar - b1(x-bar) Click here to see answer by stanbon(57303)

 Question 138864: The Rocky Mountain district sales manager of Book Publishing, Inc., a college textbook publishing company, claims that the sales representatives make an average of 45 sales calls per week on professors. Several reps say that this estimate is too low. To investigate, a random sample of 32 sales representatives reveals that the mean number of calls made last week was 46. The standard deviation of the sample is 3.3 calls. Using the .05 significance level, can we conclude that the mean number of calls per salesperson per week is more than 45? Click here to see answer by stanbon(57303)

 Question 138863: 12.47 Regression analysis of free throws by 29 NBA teams during the 2002–2003 season revealed the fitted regression Y = 55.2 + .73X (R2 = .874, syx = 53.2) where Y = total free throws made and X = total free throws attempted. The observed range of X was from 1,620 (New York Knicks) to 2,382 (Golden State Warriors). (a) Find the expected number of free throws made for a team that shoots 2,000 free throws. (b) Do you think that the intercept is meaningful? Hint: Make a scatter plot and let Excel fit the line. (c) Use the quick rule to make a 95 percent prediction interval for Y when X = 2,000. Click here to see answer by stanbon(57303)

 Question 138909: 1. Ages for the 2005 Boston Red Sox pitchers are shown below. (a) Assuming this is a random sample of major league pitchers, at the 5 percent level of significance does this sample show that the true mean age of all American League pitchers is over 30 years? State your hypotheses and decision rule and show all work. (b) If there is a difference, is it important? (c) Find the p-value and interpret it. Ages of Boston Red Sox Pitchers, October 2005 Arroyo 28 Foulke 33 Mantei 32 Timlin 39 Clement 31 Gonzalez 30 Miller 29 Wakefield 39 Embree 35 Halama 33 Myers 36 Wells 42 2. In Utica, Michigan, 205 of 226 school buses passed the annual safety inspection. In Detroit, Michigan, only 151 of 296 buses passed the inspection. (a) State the hypotheses for a right-tailed test. (b) Obtain a test statistic and p-value. (c) Is normality assured? (d) If significant, is the difference also large enough to be important? 3. Prof. Green’s multiple-choice exam had 50 questions with the distribution of correct answers shown below. Research question: At α = .05, can you reject the hypothesis that Green’s exam answers came from a uniform population Correct Answer Frequency A 8 B 8 C 9 D 11 E 14 Total 50 Click here to see answer by stanbon(57303)

 Question 138915: There are 3 red and 7 black marbles in a bag. If I am blindfolded, how many times must I reach in and pull out a marble before I am sure it is a black one? Click here to see answer by edjones(7569)

 Question 138919: All possible samples of size n are selected from a population and the mean of each sample is calculated. What is the value of the mean of the sample means? a. 0Smaller than the population mean b. 0Larger than the population mean c. 0Exactly the same as the population mean d. 0It cannot be determined in advance e. 0None of the above Click here to see answer by oscargut(891)

 Question 138914: In order to use the test statistic for the difference between two sample means both samples must have a population of at least 30 and the samples must be from dependent populations. Is this answer true or false? Click here to see answer by stanbon(57303)

 Question 138930: in a burger chain customers who use mustard are 80%, who use ketchup are 75% and who use both are 65%. what is the probability that the customers comming in the shop will use mustard, ketchup or both? Click here to see answer by stanbon(57303)

 Question 138949: In Dallas, some fire trucks were painted yellow (instead of red) to heighten their visibility. During a test period, the fleet of red fire trucks made 153,348 runs and had 20 accidents, while the fleet of yellow fire trucks made 135,035 runs and had 4 accidents. At α = .01, did the yellow fire trucks have a significantly lower accident rate? (a) State the hypotheses. (b) State the decision rule and sketch it. (c) Find the sample proportions and z test statistic. (d) Make a decision. (e) Find the p-value and interpret it. (f ) If statistically significant, do you think the difference is large enough to be important? If so, to whom, and why? (g) Is the normality assumption fulfilled? Explain. Accident Rate for Dallas Fire Trucks Statistic Red Fire Trucks Yellow Fire Trucks Number of accidents x1 = 20 accidents x2 = 4 accidents Number of fire runs n1 = 153,348 runs n2 = 135,035 runs Click here to see answer by stanbon(57303)

 Question 138984: A researcher believes that the average production in manufacturing has increased by 200 units. The hypothesis statement for this situation is: a. 0H0:  = 200 HA:   200 b. 0H0:   200 HA:  < 200 c. 0H0:  < 200 HA:  > 200 d. 0None of the above Click here to see answer by stanbon(57303)

 Question 138983: The following hypotheses is an example of: HO: p ≤ .40 HA: p > .40 a. 0A one-tail test for means b. 0A two-tail test for means c. 0A one-tail test for proportions d. 0A two-tail test for proportions e. 0None of the above Click here to see answer by stanbon(57303)

 Question 138998: An expert witness in a case of alleged racial discrimination in a state university school of nursing introduced a regression of the determinants of Salary of each professor for each year during an 8-year period (n = 423) with the following results, with dependent variable Year (year in which the salary was observed) and predictors YearHire (year when the individual was hired), Race (1 if individual is black, 0 otherwise), and Rank (1 if individual is an assistant professor, 0 otherwise). Click here to see answer by stanbon(57303)

 Question 138982: The z-test statistic is used when performing a small sample test of variances. 0True 0False Click here to see answer by stanbon(57303)

 Question 138977: A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were 3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.400 3.437 3.477 (a) Construct a 90 percent confidence interval for the true mean weight. (b) What sample size would be necessary to estimate the true weight with an error of + 0.03 grams with 90 percent confidence? (c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture Click here to see answer by stanbon(57303)

 Question 138929: in a burger chain, customers who use mustard are 80% customers whwo use ketchup are 65% what is the probability that customers comming in the burger shop will use mustard, ketchup or both? Click here to see answer by stanbon(57303)

 Question 138921: The following hypotheses is an example of: HO: m ≠ .40 HA: m = .40 a. 0A one-tail test for means b. 0A two-tail test for means c. 0A one-tail test for proportions d. 0A two-tail test for proportions e. 0None of the above Click here to see answer by stanbon(57303)

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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