Let events A and B and sample space S be definedas the following intervals:S = {x: -1 ≤ x ≤ 12}A = {x: 0 < x < 6}B = {x: 3 ≤ x ≤ 7}Characterize the following events:a) An Bb) AU Bc) An BC

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Answered: Let events A and B and sample space S…

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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Let X be the number of blueberries on a muffin made by Michael, and denote by m to be its median. Charles suspects that Michael has been adding more blueberries than usual to his muffins. For some reason, he has kept meticulous records. The last 15 muffins Charles bought contained the following numbers of blueberries: 96 12 8 15 7 8 12 6 10 13 11 11 10 10 Charles would like to test Ho: m = 9 against H₁: m>9 at significance level a = 0.1. (a) Use the sign test to test the hypothesis. (b) Use the Wilcoxon sign-rank test to test the hypothesis. (Note: Assume that the distribution is continuous) (c) Use the t-test to test the hypothesis, assuming the underlying distribution is symmetric.
can you solve this for me by showing step by step for each question? Acme Food manufactures and sells bags of doughnuts whose weights follow a normal distribution with a mean of 400g and standard deviation 8g. a) Find the probability that a bag of doughnuts weights less than 410g b) Find P (X>412) c) Find P (395 < X < 404) d) The company can be prosecuted if the bags are less than 380g, if the company sells 50 bags per day find the expected number of bags under this weight. e) On a typical day 1.22% of bags are rejected as they are too heavy. Find the rejection weight.
Consider ratings of 4 “Agree” or 5 “Strongly Agree” to mean that test takers have obtained a “high” score on a BRS item. Ratings of 1-3 would be considered “low” item scores. Compute the item discrimination index (d) for BRS Item 3. Enter the values below that you obtain from Excel: Total # of test takers N = _______ 25% of the total # of test takers, or # in the Upper 25% group U = _______ # of test takers in the Upper 25% group for BRS total scores who scored high on item 3 = _______ # of test takers in the Lower 25% group for BRS total scores who scored high on item 3 = _______ Item discrimination index d = ________ ID # Item 1 Item 2 Item 3 Item 4 Item 5 Item 6 BRS Total Score 25 5 5 5 5 5 5 55 24 5 5 2 4 5 5 50 21 5 4 5 3 5 5 48 22 5 5 4 3 3 4 46 23 5 3 3 5 5 2 46 18 4 5 5 4 4 4 44 20 5 5 4 3 3 4 44 16 5 4 5 5 4 3 42 19 4 5 4 1…
D5) X and Y are two points that are selected according to a uniform distribution. Calculate the expected value of the distance between these two points for each of the following cases: a) Both X and Y are selected independently from the range 0-1. b) We select X between 0 and 1 and then select Y between 0 and X. Note: For case b the distance is equal to |Y-X|
n a big university with over 10,000 students, 20% of all students work full time. A random sample of 100 students is selected from the university. Let X denote the number of students who work full time in the sample. b) Find ?(? = 20) c) Find ?(? ≤ 20) d) Find ?(? ≥ 20) Can you explain how you got them using work?
Assume that the height, X, of a college woman is a normally distributed random variable with a mean of 65 inches and a standard deviation of 3 inches. Suppose that we sample the heights of 180 randomly chosen college women. Let M be the sample mean of the 180 height measurements. Let S be the sum of the 180 height measurements. All measurements are in inches. Using R and write the code out.a) What is the probability that X < 59? b) What is the probability that X > 59? c) What is the probability that all of the 180 measurements are greater than 59? d) What is the expected value of S? e) What is the standard deviation of S? f) What is the probability that S-180*65 >10? g) What is the standard deviation of S-180*65 h) What is the expected value of M? i) What is the standard deviation of M? j) What is the probability that M >65.41? k) What is the standard deviation of 180*M? l) If the probability of X > k is equal to .3, then what is k?
Randomly selected students were given five seconds to estimate the value of a product of numbers with the results shown below. Estimates from students given 1 x 2 × 3 x 4 x 5 x 6 x 7 x 8: 500, 150, 500, 42200, 560, 25, 5000, 842, 2000, 600 Estimates from students given 8 x 7 x 6 x 5 x 4 × 3 × 2 × 1: 450, 3600, 42000, 52836, 400, 40000, 2000, 5000, 428, 25000 Use a 0.05 significance level to test the claim that the two populations have the same mean. (a) The standardized test statistic is (b) The conclusion is O A. There is sufficient evidence to warrant the rejection of the claim that the two populations have the same mean O B. There is not sufficient evidence to warrant the rejection of the claim that the two populations have the same mean

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Let events A and B and sample space S be defined as the following intervals: S = {x: -1 ≤ x ≤ 12} A = {x: 0 < x < 6} B = {x: 3 ≤ x ≤ 7} Characterize the following events: a) An B b) AU B c) An BC