Basic Computation: hat p Distribution Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (b) Suppose n= 20 and p=0.23. Can we safely approximate the hat{p} distribution by a normal distribution? Why or why not?

Question
Normal distributions
asked 2021-02-16
Basic Computation: hat p Distribution Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.
(b) Suppose \(n= 20\) and \(p=0.23\). Can we safely approximate the \hat{p} distribution by a normal distribution? Why or why not?

Answers (1)

2021-02-17
We have binomial experiment with \(n = 20\) and \(p = 0.23\)
\(np = 20(0.23)\)
\(np = 4.6\)
\(nq = 20(1 — 0.23)\)
\(nq = 15.4\)
Since both the values np and nq are not greater than 5, hence, we cannot approximate the \(\hat{p}\) distribution by a normal distribution.
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