Question

Rolling a six-sided die 74 times and recording the number of odd numbers rolled.

Determine whether or not the given procedure resilts in a binomial distribution. If not, identify which condition is not met.

Answer 1

Binomial

Explanation:

Given that a six sided die is rolled 74 times.

When a fair die is rolled number of outcomes are 6 out of which 3 are odd and 3 even.

Pro (getting odd) = Prob (getting even) = 0.5

Also each throw is independent of the other

Hence X - no of throws which resulted in odd numbers is Binomial with

n = 74 and p = 0.5

Mean = 37 and variance = 18.5

(all conditions for binomial are met)

(There are two outcomes either odd or even and each trial is independent of the other)