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 = 44 and p = 0.23. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.) np = nq = ---Select--- , p̂ ---Select--- be approximated by a normal random variable because ---Select--- . 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? ---Select--- , p̂ ---Select--- be approximated by a normal random variable because ---Select--- . (c) Suppose n = 55 and p = 0.25. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.) np = nq = ---Select--- , p̂ ---Select--- be approximated by a normal random variable because ---Select--- . What are the values of μp̂ and σp̂? (Use 3 decimal places.) μp̂ = σp̂ =

Answer 1

a) np = 44 * 0.23 = 10.12

nq = 44 * (1-0.23) = 33.88

can be approximated by a normal random variable because np and nq are greater than 5.

b) np = 25 * 0.15 = 3.75

nq = 25 * (1-0.15) = 21.25

cannot be safely approximated by a normal random variable because np is less than 5.

c) np = 55 * 0.25 = 13.75

nq = 55 * (1-0.25) = 41.25

can be approximated by a normal random variable because np and nq are greater than 5.

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