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Suppose we have a binomial experiment in which success is defined to be a particular quality...

Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.

(a) Suppose n = 39 and p = 0.24. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.)

np =
nq =

(YES or NO), p̂ (CANNOT or CAN) be approximated by a normal random variable because .(NP exceeds, np does not exceed, nq exceeds, nq does not exceed, np and nq do not exceed, or both np and nq exceed.)

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?
(YES or NO), p̂ (CANNOT or CAN) be approximated by a normal random variable because (NP exceeds, np does not exceed, nq exceeds, nq does not exceed, np and nq do not exceed, or both np and nq exceed.).

(c) Suppose n = 53 and p = 0.23. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.)

np =
nq =


(YES or NO), p̂ (CANNOT or CAN) be approximated by a normal random variable because (NP exceeds, np does not exceed, nq exceeds, nq does not exceed, np and nq do not exceed, or both np and nq exceed.).

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

μp̂ =
σp̂ =
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