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 = 35 and p = 0.17. 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 and nq do not exceed, or np does not exceed, or both np and nq exceed, or nq does not exceed, or nq exceeds, or np exceeds) ________ .

What are the values of μ_p̂ and σ_p̂? (Use 3 decimal places.)

μ_p̂ =

σ_p̂ =

(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 and nq do not exceed, or np does not exceed, or both np and nq exceed, or nq does not exceed, or nq exceeds, or np exceeds) ________ .

(c) Suppose n = 46 and p = 0.38. 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 and nq do not exceed, or np does not exceed, or both np and nq exceed, or nq does not exceed, or nq exceeds, or np exceeds) ________ .

What are the values of μ_p̂ and σ_p̂? (Use 3 decimal places.)

μ_p̂ =

σ_p̂ =

Answer 1