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= 25 and p= 0.15. Can we safely approximate the hat{p} distribution by a normal distribution? Why or why not?

Chardonnay Felix 2021-02-25 Answered
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 \(n= 25\) and \(p= 0.15\). Can we safely approximate the \(\hat{p}\) distribution by a normal distribution? Why or why not?

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Benedict
Answered 2021-02-26 Author has 27710 answers
We have binomial experiment with \(n = 25\) and \(p = 0.15\)
\(np = 25(0.15)\)
\(np = 3.75\)
\(nq=25(1-0.15)\)
\(nq=21.25\)
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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