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Suppose that the test score of a student taking the final of a probability course is a random variable with mean 75. (a) Give an upper bound for the probability that a student's test score will exceed 85. P{score > 85}< 0.8823 (b) Suppose that we know, in addition, that the variance of students' test scores on the final is 20. What can you say about the probability that a student will score between 65 and 85 (do not use the central limit theorem)? P{65 < score < 85} 0.87 %3D (c) How many students would have to take the final to ensure with a probability of at least 0.85 that the class average would be within 5 of 75 (do not use the central limit theorem)? n = (d) If you use the central limit theorem in (c), what is your estimate for the number of students needed? n =

Suppose that the test score of a student taking the final of a probability course is a random variable with mean 75. (a) Give an upper bound for the probability that a student's test score will exceed 85. P{score > 85}< 0.8823 (b) Suppose that we know, in addition, that the variance of students' test scores on the final is 20. What can you say about the probability that a student will score between 65 and 85 (do not use the central limit theorem)? P{65 < score < 85} 0.87 %3D (c) How many students would have to take the final to ensure with a probability of at least 0.85 that the class average would be within 5 of 75 (do not use the central limit theorem)? n = (d) If you use the central limit theorem in (c), what is your estimate for the number of students needed? n =

A First Course in Probability (10th Edition)
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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Suppose that the test score of a student taking the final of a probability course is a random variable with mean 75. (a) Give an upper bound for the probability that a student's test score will exceed 85. P{score > 85}< 0.8823 (b) Suppose that we know, in addition, that the variance of students' test scores on the final is 20. What can you say about the probability that a student will score between 65 and 85 (do not use the central limit theorem)? P{65 < score < 85} 0.87 (c) How many students would have to take the final to ensure with a probability of at least 0.85 that the class average would be within 5 of 75 (do not use the central limit theorem)? (d) If you use the central limit theorem in (c), what is your estimate for the number of students needed? n =
Transcribed Image Text:Suppose that the test score of a student taking the final of a probability course is a random variable with mean 75. (a) Give an upper bound for the probability that a student's test score will exceed 85. P{score > 85}< 0.8823 (b) Suppose that we know, in addition, that the variance of students' test scores on the final is 20. What can you say about the probability that a student will score between 65 and 85 (do not use the central limit theorem)? P{65 < score < 85} 0.87 (c) How many students would have to take the final to ensure with a probability of at least 0.85 that the class average would be within 5 of 75 (do not use the central limit theorem)? (d) If you use the central limit theorem in (c), what is your estimate for the number of students needed? n =
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