Suppose a simple random sample of size n=125 is obtained from a population whose size is N=30,000 and whose population proportion with a specified characteristic is p=0.8. Complete parts (a) through(c) below.

(a) Describe the sampling distribution of

p.

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

A.

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

B.

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

C.

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

Your answer is correct.

D.

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

Determine the mean of the sampling distribution of

p.

p=

. 8

.8 (Round to one decimal place asneeded.)

Determine the standard deviation of the sampling distribution of

p.

p=

0.035777

0.035777 (Round to six decimal places asneeded.)

(b) What is the probability of obtaining x=105 or more individuals with thecharacteristic? Thatis, what is P(

p0.84)?

P(

p0.84)=

0.1318

0.1318 (Round to four decimal places asneeded.)

(c) What is the probability of obtaining x=90 or fewer individuals with thecharacteristic? Thatis, what is P(

p0.72)?

P(

p0.72)=

nothing

(Round to four decimal places asneeded.)