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5. Let X₁, X₂,..., X100 be the weights of 100 bales of hay. Assume that the random variables are i.i.d. with mean 90 pounds and standard deviation 10 pounds. Let S = X₁ + ... + X100 be their combined weight. (a) What is the mean of S? (b) What is the variance of S? (c) Approximate the probability that S exceeds 120 pounds.

5. Let X₁, X₂,..., X100 be the weights of 100 bales of hay. Assume that the random variables are i.i.d. with mean 90 pounds and standard deviation 10 pounds. Let S = X₁ + ... + X100 be their combined weight. (a) What is the mean of S? (b) What is the variance of S? (c) Approximate the probability that S exceeds 120 pounds.

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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5. Let \( X_1, X_2, \ldots, X_{100} \) be the weights of 100 bales of hay. Assume that the random variables are i.i.d. with mean 90 pounds and standard deviation 10 pounds. Let \( S = X_1 + \ldots + X_{100} \) be their combined weight. (a) What is the mean of \( S \)? (b) What is the variance of \( S \)? (c) Approximate the probability that \( S \) exceeds 120 pounds.
Transcribed Image Text:5. Let \( X_1, X_2, \ldots, X_{100} \) be the weights of 100 bales of hay. Assume that the random variables are i.i.d. with mean 90 pounds and standard deviation 10 pounds. Let \( S = X_1 + \ldots + X_{100} \) be their combined weight. (a) What is the mean of \( S \)? (b) What is the variance of \( S \)? (c) Approximate the probability that \( S \) exceeds 120 pounds.
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