Question

# 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.

Normal distributions

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?

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.