Let A denote the event that the next request for assistance from a statistical software consultant relates to the SPSS package, and let B be the event that the next request is for help with SAS. Suppose that P(A) = 0.20 and P(B) = 0.40. (There are various packages suchas Minitab, SPSS, SAS, JMP, and R.)(a) Why is it not the case that P(A) + P(B) = 1?O The probabilities do not add to 1 because they are independent events.O The probabilities should add to 1; P(A) or P(B) must be recorded incorrectly.O The probabilities do not add to 1 because there are other software packages for which requests could be made.O The probabilities are not mutually exclusive and thus they do not need to add to 1.O The probabilities do add to 1.(b) Calculate P(A').(c) Calculate P(A U B).(d) Calculate P(A' N B').

Answered: Image /qna-images/answer/d8308cb2-7848-4c00-8ade-aed0bcb82ba3.jpg

Answered: Let A denote the event that the next…

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 X1, X2, and X3 represent the times necessary to perform three successive repair tasks at a certain service facility. Suppose they are independent, normal rv's with expected values ?1, ?2, and ?3 and variances ?12, ?22, and ?32, respectively. (Round your answers to four decimal places.) (a) If ?1 = ?2 = ?3 = 60 and ?12 = ?22 = ?32 = 18, calculate P(To ≤ 204) and P(144 ≤ To ≤ 204). P(To ≤ 204) = P(144 ≤ To ≤ 204) = (b) Using the ?i's and ?i's given in part (a), calculate both P(54 ≤ X) and P(58 ≤ X ≤ 62). P(54 ≤ X) = P(58 ≤ X ≤ 62) = (c) Using the ?i's and ?i's given in part (a), calculate P(−12 ≤ X1 − 0.5X2 − 0.5X3 ≤ 6). P(−12 ≤ X1 − 0.5X2 − 0.5X3 ≤ 6) =
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The National Academy of Science reported that 41% of research in mathematics is published by US authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 41%. He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 186 recent articles published by reputable mathematics research journals and finds that 92 of these articles have US authors. Does this evidence support the mathematics chairperson’s claim that the percentage is no longer 41%? Use a 0.05 level of significance. Step 1 of 3: State the null and alternative hypotheses for the test. circle the answer below. H0 p=0.41 ha: p⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯0.41 A.<B.≠C.> Step 2 of 3: Compute the value of the test statistic. Round your answer to two decimal places Step 3 of 3: Draw a conclusion and interpret the decision. A. We reject the null hypothesis and conclude that there is insufficient evidence at a…
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Need help with parts (a) to (d) on this Intro to Probability and Statistics homework problem. Make sure the answers you provide are lengthy. Don't give short answers. Also, make sure your handwriting is neat and readable. Statistically speaking, the typical romantic couple spends 3 hours of qualitytime together each day, with a variance of 1.5 hours. During my teenageyears, I was under the assumption that a friend and I were a couple, but sherecently pushed back on that claim. So, I logged our time spent together over aperiod of 92 days. As it turned out, we spent 2.65 hours together on a typicalday, again with a variance of 1.5 hours. Assuming that all of the time we spendtogether is “quality” and that relationship time spent is governed by the normaldistribution, do I have sufficient statistical evidence to claim that we were, infact, in a romantic relationship? (a) Find and interpret the z-score of our time spent together, specificallyreferencing what information the sign…
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You own a company called Company X, which has monthly sales that are independent normal random variables with mean 100 and variance 10. Your rival company, called Company Y, has monthly sales that are independent normal random variables with mean 110 and variance 20. (a) Find the probability that your company, Company X, makes more than $307 this quarter (a quarter is 3 months). (b) What is the probability that your company makes more money than your rival company this month?
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