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A fair die is rolled 8 times.a. What is the probability
Chapter 4, Problem 6E(choose chapter or problem)
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.
Questions & Answers
QUESTION:
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.
ANSWER: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