Suppose we have a binomial experiment in which success is defined to be a partic
ID: 3171116 • Letter: S
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 = 25 and p = 0.39. Can we approximate p^ by a normal distribution? Why? (Use 2 decimal places.)
---Select--- Yes No
Yes
, p^ ---Select--- cannot can
can
be approximated by a normal random variable because ---Select--- both np and nq exceed np and nq do not exceed np does not exceed nq exceeds np exceeds nq does not exceed
both np and nq exceed
.
What are the values of p^ and p^? (Use 3 decimal places.)
(b) Suppose n = 25 and p = 0.15. Can we safely approximate p^ by a normal distribution? Why or why not?
---Select--- Yes No
No
, p^ ---Select--- can cannot
cannot
be approximated by a normal random variable because ---Select--- nq does not exceed nq exceeds np exceeds np and nq do not exceed np does not exceed both np and nq exceed
np does not exceed
.
(c) Suppose n = 48 and p = 0.35. Can we approximate p^ by a normal distribution? Why? (Use 2 decimal places.)
---Select--- Yes No
Yes
, p^ ---Select--- cannot can
can
be approximated by a normal random variable because ---Select--- np does not exceed nq exceeds both np and nq exceed np exceeds nq does not exceed np and nq do not exceed
both np and nq exceed
.
What are the values of p^ and p^? (Use 3 decimal places.)
Explanation / Answer
a)np=25*0.39=9.75
nq=15.75
no cannot be approximated by a normal random variable because np does not exceed
b)np=25*0.15=3.75
nq=25*0.85=21.25
No cannot be approximated by a normal random variable because np does not exceed
c)np=48*0.35=16.8
n1=48*0.65=31.2
yes
can
be approximated by a normal random variable because both np and nq exceed
here p =np=16.8
p =(np(1-p))1/2=3.305
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