Question

Suppose a simple random sample of size n=75 is obtained from a population whose size is N=15,000 and whose population proportion with a specified characteristic is p=0.8.

a) Determine the mean of the sampling distribution of p with caret.

Determine the standard deviation of the sampling distribution of p with caret.

b) What is the probability of obtaining x=66 or more individuals with the​ characteristic? That​ is, what is ​P(p with caret greater than or equals 0.88)?

What is the probability of obtaining x=57 or fewer individuals with the​ characteristic? That​ is, what is ​P(p with caret less than or equals 0.76​)?

Answer 1

a) Determine the mean of the sampling distribution of p with caret.

Determine the standard deviation of the sampling distribution of p with caret.

The following information has been provided about the population proportion and the sample size:

Population Proportion =	0.8
Sample Size =	75

the population men of sample proportions and the corresponding standard error are:

Observe that:

which indicates that the assumption for normal approximation for the sampling distribution is met.

We need to compute . Based on the information provided,

Now, the following is obtained using normal approximation:

We need to compute . Based on the information provided, the population men of sample proportions and the corresponding standard error are: