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A fair die is rolled 8 times.a. What is the probability

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 6E Chapter 4.2

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 6E

A fair die is rolled 8 times.

a. What is the probability that the die comes up 6 exactly twice?

b. What is the probability that the die comes up an odd number exactly five times?

c. Find the mean number of times a 6 comes up.

d. Find the mean number of times an odd number comes up.

e. Find the standard deviation of the number of times a 6 comes up.

f. Find the standard deviation of the number of times an odd number comes up.

Step-by-Step Solution:

Answer :

Step 1 of 7:

Given, a fair die rolled 8 times

A die will be having 6 sides

Let X follows binomial distribution with probability mass function is

P(x: n,p) =  (1 - p , x = 0, 1, 2, ….., n.

Mean of the binomial distribution is

   = np

Variance of the binomial distribution is

   = npq

Where, n = 8 and p = 1/6


Step 2 of 7

Chapter 4.2, Problem 6E is Solved
Step 3 of 7

Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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A fair die is rolled 8 times.a. What is the probability