Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.
(a) Suppose n = 41 and p = 0.34. 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 does not exceed np does not
exceed both np and nq exceed nq exceeds np and nq do not exceed np
exceeds .
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--- Yes No
, p̂ ---Select--- cannot can be
approximated by a normal random variable
because ---Select--- nq exceeds np and nq do not exceed
np does not exceed np exceeds nq does not exceed both np and nq
exceed .
(c) Suppose n = 63 and p = 0.17. 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 does not exceed np
and nq do not exceed both np and nq exceed np does not exceed nq
exceeds .
What are the values of μp̂ and
σp̂? (Use 3 decimal places.)
μp̂ = |
σp̂ = |
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