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 :

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