Answer to Question #63722 in Statistics and Probability for shelley

Question

Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.
(a) Suppose n = 36 and p = 0.23. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.)
np =
nq =

, p̂ be approximated by a normal random variable because .

What are the values of μp̂ and σp̂? (Use 3 decimal places.)
μp̂ =
σp̂ =

(b) Suppose n = 25 and p = 0.15. Can we safely approximate p̂ by a normal distribution? Why or why not?
, p̂ be approximated by a normal random variable because .

(c) Suppose n = 58 and p = 0.21. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.)
np =
nq =

, p̂ be approximated by a normal random variable because .

What are the values of μp̂ and σp̂? (Use 3 decimal places.)
μp̂ =
σp̂ =