# 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 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? 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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(b)$$n=300$$,$$p=.05$$ Np>5 and nq>5, estimate P(at least 11) with n=13 and p = 0.6 by using the normal distributions as an approximation to the binomial distribution. if $$\displaystyle{n}{p}{<}{5}{\quad\text{or}\quad}{n}{q}{<}{5}$$ then state the normal approximation is not suitable.
p (at least 11) = ? (d)$$n=1000$$,$$p=.001$$ (с)$$n=500$$,$$p=.001$$ (a)$$n=40$$,$$p=.05$$