According to the 2000 U. S. Census, 80% of Americans over the age of 25 have earned a high school diploma. Suppose we take a random sample of 120 Americans and record the proportion, p, of individuals in our sample that have a high school diploma.

a) The mean is 0.8.

b) The standard deviation is 0.0365.

c) Normal

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation

80% of Americans over the age of 25 have earned a high school diploma.

This means that

Suppose we take a random sample of 120 Americans

This means that .

Question a:

The mean is:

The mean is 0.8.

Question b:

The standard deviation is:

The standard deviation is 0.0365.

Question c:

By the Central Limit Theorem, approximately normal.

they are simplified

step-by-step explanation: