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 = 5.4

nq = 24.6

Yes  , p̂ 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   . Enter an exact number.

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?
No  , p̂ cannot  be approximated by a normal random variable because np does not exceed . Enter an exact number

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

np = 15.08

nq = 42.92

Yes , p̂  can be approximated by a normal random variable because both np and nq exceed . Enter an exact number

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

μ_p̂ =  

σ_p̂ =  

Answer 1