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 = 30 and p = 0.18. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.)

np =

nq =

---Select--- Yes No , p̂  ---Select--- cannot can be approximated by a normal random variable because  ---Select--- nq does not exceed np does not exceed both np and nq exceed nq exceeds np exceeds np and nq do not exceed  .

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?
---Select--- Yes No , p̂  ---Select--- can cannot be approximated by a normal random variable because  ---Select--- both np and nq exceed np does not exceed nq does not exceed np exceeds np and nq do not exceed nq exceeds  .

(c) Suppose n = 58 and p = 0.26. Can we approximate p̂ by a normal distribution? Why? (Use 2 decimal places.)

np =

nq =

---Select--- Yes No , p̂  ---Select--- can cannot be approximated by a normal random variable because  ---Select--- np and nq do not exceed np exceeds np does not exceed both np and nq exceed nq does not exceed nq exceeds

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

μ_p̂ =

σ_p̂ =

Answer 1