Four buses carrying 153 high school students arrive to Montreal. The buses carry, respectively, 34, 44, 32, and 43 students. One of the studetns is randomly selected. LetX denote the number of students that were on the bus carrying this randomly selected student. One of the 4 bus drivers is also randomly selected. Let X denote thenumber of students on his bus. Compute the expectations and variances of X and Y:E(X) = |Var(X)E(Y)Var(Y) =

Four buses carrying 153 high school students arrive to Montreal. The buses carry, respectively, 34,…

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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2. Suppose that X1, X2, X3 and X4, are independent and identically distributed with a mean of 2.5 and a standard deviation of 0.6. Find the mean and standard deviation for variables Y and W defined below. Let Y= 4X1 а. b. Let W= Xi + X2 + X3 + X4
The Admission director for a college far from mart and town believes that an inverse relationship exists between a private college's average discount rate(determined by the average amount of scholarships students receive) and the annual yield (the percentage of admitted students who actually attend). The Director's independent variable is a private college's discount rate measured as a percentage, and the dependent variable is the college's annual yield measured as a percentage. The following results were obtained for a sample of 30 private colleges: x- Discount rate(percentage) - range: 35 to 72 percent y- Annual Yield(percentage) - range: 12 o 81 percent Σxi = 1612 Σyi = 898 Σxiyi = 44,377 Σxi2 = 89,790 Σyi2 = 35,704 a. Calculate the sample regression line's slope estimate. Interpret the sample regression line's slope estimate. b. Calculate the sample regression line's intercept estimate. Interpret the sample regression line's intercept estimate. Assume the following sum of…
Can a low barometer reading be used to predict maximum wind speed of an approaching tropical cyclone? For a random sample of tropical cyclones, let x be the lowest pressure (in millibars) as a cyclone approaches, and let y be the maximum wind speed (in miles per hour) of the cyclone. x 1,004 975 992 935 971 924 y 40 100 65 145 77 154 Use a calculator to verify that x = 5,801, x2 = 5,613,547, y = 581, y2 = 66,495 and xy = 554,778.Compute r. (Round your answer to four decimal places.)r = As x increases, does the value of r imply that y should tend to increase or decrease? Explain your answer.Given our value of r, y should tend to remain constant as x increases.Given our value of r, y should tend to decrease as x increases. Given our value of r, y should tend to increase as x increases.Given our value of r, we can not draw any conclusions for the behavior of y as x increases.
A restaurant manager is planning a new layout for the tables in his store. He will be placing tables of 2, tables of 4, and tables of 6 throughout the dining room. To help him decide how many of each he needs, he decides to keep track of all table requests by customers during a 2-week period. Which measure of central tendency would BEST indicate the typical table size needed?
A variable of two populations has a mean of 30 and a standard deviation of 18 for one of the populations and a mean of 30 and a standard deviation of 32 for the other population. Complete parts (a) through (c). a. For independent samples of size 9 and 16, respectively, find the mean and standard deviation of X₁ -X₂. (Assume that the sampling is done with replacement or that the population is large enough.) The mean of X₁ -X₂ is. (Type an integer or a decimal. Do not round.) The standard deviation of X₁-X₂ is (Round to four decimal places as needed.) b. Must the variable under consideration be normally distributed on each of the two populations for you to answer part (a)? Choose the correct answer below. OA. No, the variable does not need to be normally distributed for the formulas for the mean and standard deviation of x₁-x₂ to hold as long as the sample sizes are large enough, as long as the sampling is done with replacement. B. No, the formulas for the mean and standard deviation of…
3. Let X Pois(4). Find the distribution of Y = √X.
A statistical program is recommended. The Jacobs Chemical Company wants to estimate the mean time (minutes) required to mix a batch of material on machines produced by three different manufacturers. To limit the cost of testing, four batches of material were mixed on machines produced by each of the three manufacturers. The times needed to mix the material follow. Manufacturer 1 Manufacturer 2 Manufacturer 3 1 21 0 P₂- 27 (a) Define all variables. X₁ 25 23 X₂ 0 Moi Bo = 0 H₂:0 27 Ho: Poo H₂: Po=0 25 30 26 Manufacturer 1 2 3 19 18 Write a multiple regression equation that can be used to analyze the data. E(y) = 22 (b) What are the best estimates of the coefficients in your regression equation? Po - 21 (c) In terms of the regression equation coefficients, what hypotheses must we test to see whether the mean time to mix a batch of material is the same for all three manufacturers? Hoi B₁-B₂=0 H: One or more of the parameters is not equal to zero. OH: One or more of the parameters is not…
In order to use the defining formula for variance, we must calculate (x − x)2 for each data value in the data set 14, 18, 22, 26, 33. Use the values in the data set and the mean x = 22.6 to fill out the following table. x 14 18 22 26 33 x 22.6 22.6 22.6 22.6 22.6 x − x 14 − 22.6 = −8.6 18 − 22.6 = __________ 22 − 22.6 = −0.6 26 − 22.6 = _________ 33 − 22.6 = 10.4 (x − x)2 73.96 __________ 0.36 ________ 108.16
An experiment where a patient's blood pressure is measured before a treatment (call it X;) and after the treatment (call it Y;). The difference in the blood pressue of each patient, Z; = Y; – X; is also recorded. The sample size n of patients is large. Suppose the true population mean of the patient's blood pressure before treatment is 41 and after treatment is 42, both unknown. Suppose the true population variance of the patient's blood pressue before and after treatment are the same, but unknown. Find an approximate 1-a confidence interval for 12 - 41- 2.

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