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

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

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.