H1 Math - Help!

A sample of n pens is observed and the number of pens is denoted by X.

Assume that X has the distribution B(n,p).

Sixty samples of 15 pens with p=0.15 are taken, find the probability that the mean number of blue pens per sample of 15 is between 2 and 6 inclusive.

Do I do CLT since distribution is non-normal? Ans: 0.919.

Hi,

In the context of this problem, X ~ B(15, 0.15), so

E(X) = 15(0.15) and

Var(X) = 15(0.15)(0.85).

Since sample size = 60 > 50, we apply CLT to obtain X-bar which will follow a normal distribution with

mean = E(X) and

variance = Var(X) / 60.

The remaining steps should be straightforward with GC. Thanks.

Cheers,
Wen Shih