A fair die is rolled 360 times.

Question

A fair die is rolled 360 times.

(a) What is the expected number (mean) of the number of times a 2 will

be rolled?

(b) What is the standard deviation of the number of times a 2 will be

rolled?

Answer 1

Hi Julie,

 

Rolling a die and looking for a specific number as a result gives a binomial distribution. There are only two possible results (that you care about): 2 and not-2, and the probability of rolling a 2 never changes.

 

The expected value of a binomial distribution is E[x] = np, and the standard deviation is SD[x] = √(npq) where n is the number of trials (rolls), p is the probability of success (rolling a 2) and q is the complement of p (1-p, not rolling a 2).

 

For this problem, you have

n = 360

p = 1/6

q = 5/6

 

E[x] = np = 360*1/6 = 60

SD[x] = √(npq) = √(360*1/6*5/6) = √(50) ≈ 7.07