Distribution Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.(a) Suppose n = 100 and p= 0.23. Can we safely approximate the hat{p} distribution by a normal distribution? Why? Compute mu_{hat{p}} and sigma_{hat{p}}.

Braxton Pugh 2020-10-21 Answered

Distribution Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.
(a) Suppose n=100 and p=0.23. Can we safely approximate the p^ distribution by a normal distribution? Why?
Compute μp^ and σp^.

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Expert Answer

berggansS
Answered 2020-10-22 Author has 91 answers

We have binomial experiment with n=100 and p=0.23
np=100(0.23)
np=23
nq=100(10.23)
nq=77
Since both the values np and ng are greater than 5, hence, we can approximate the p^ distribution by a normal distribution.
The formula for the mean of the p^ distribution is μp^=p^.
μp^=0.23
The formula for the standard error of the normal approximation to the p^ distribution is
σp^=pqn
σp^=0.2310.23100
σp^=0.042

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