Suppose a simple random sample of size n=200 is obtained from a population whose size is N=10,000 and whose population proportion with a specified characteristic is p=0.8.

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(a) Describe the sampling distribution of

p.

Choose the phrase that best describes the shape of the sampling distribution below.

A.

Approximately normal because n0.05N and np(1p)<10.

B.

Not normal because n0.05N and np(1p)<10.

C.

Not normal because n0.05N and np(1p)10.

D.

Approximately normal because n0.05N and np(1p)10.

Determine the mean of the sampling distribution of

p.

p=

nothing

(Round to one decimal place asneeded.)

Determine the standard deviation of the sampling distribution of

p.

p=

nothing

(Round to six decimal places asneeded.)

(b) What is the probability of obtaining x=168 or more individuals with thecharacteristic? Thatis, what is P(

p0.84)?

P(

p0.84)=

nothing

(Round to four decimal places asneeded.)

(c) What is the probability of obtaining x=158 or fewer individuals with thecharacteristic? Thatis, what is P(

p0.79)?

P(

p0.79)=

nothing

(Round to four decimal places asneeded.)