Question

A die is rolled 23 times and the number of twos that come up is tallied. If this experiment is repeated many times, find the standard deviation for the number of twos.

19.2
1.8
2.4
5.8

Answer 1

The probability of rolling a 2 is 1/6. If X is a random variable representing the number of 2s that are obtained after rolling a die 23 times, then X follows a binomial distribution with success probability p = 1/6 across n = 23 trials.

The variance of a binomial distribution with parameters p and n is n p (1 - p), so the standard deviation in this case would be

√(23 • 1/6 • 5/6) ≈ 1.8