Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us. (a) Suppose n = 25 and p = 0.25. Can we approximate p̂ by a normal...

(a) Suppose
n
= 25 and
p
= 0.25. 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 exceeds nq exceeds both np and nq exceed nq does not exceed np does not exceed np and nq do not exceed .


What are the values of μ_p̂
and σ_p̂? (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--- Yes No , p̂  ---Select--- can cannot be approximated by a normal random variable because  ---Select--- nq does not exceed nq exceeds np exceeds both np and nq exceed np does not exceed np and nq do not exceed .


(c) Suppose
n
= 42 and
p
= 0.37. 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--- nq exceeds nq does not exceed np and nq do not exceed both np and nq exceed np does not exceed np exceeds .


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

μp̂ =

σp̂ =