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