Question

Suppose a simple random sample of size n+75 is obtained from a population whose size is N=10,000 and whose population proportion with a specified characteristic is p= 0.6 . 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 n<_ 0.05N and np(1-p)<10.

B.) Approximately normal because n<_0.05N and np(1-p)>_10.

C). Not normal because n<_0.05N and np(1 -p)>_10.

D). Approximately normal because n<_ 0.05N and np(1-p)< 10.

Determine the mean of the sampling distribution of p^.

μ^p=_______

​(Round to one decimal place as​ needed.)

Determine the standard deviation of the sampling distribution of p^

σ^p=______

​(Round to six decimal places as​ needed.)

​(b) What is the probability of obtaining x=48 or more individuals with the​ characteristic? That​ is, what is ​

P(p^>_0.64)=

​(Round to four decimal places as​ needed.)

​(c) What is the probability of obtaining x=36 or fewer individuals with the​ characteristic? That​ is, what is ​P((p^<_0.48)=____

Answer 1