Question

Births There are about 11,000 births each day in the United States, and the proportion of boys born in the United States is 0.512. Assume that each day, 100 births are randomly selected and the proportion of boys is recorded.

a. What do you know about the mean of the sample proportions?

b. What do youknow about the shape of the distribution of the sample proportions?

Short answer

a. The mean of the sample proportion should be equal to the population proportion; that is, the mean value should be equal to 0.512.

b. The distribution of the sample proportions should be approximately bell-shaped.

Step-by-step solution

Given information

It is given that the population proportion of boys born in the United States is equal to 0.512.

A sample of 100 births is selected each day, and the proportion of boys is recorded.

Mean of the sample proportions

a.

It is known that the mean of sample proportions is equal to the population proportion.

Here, the population proportion of boys is equal to 0.512.

The mean of the sample proportions of boys should be approximately equal to 0.512.

Shape of the distribution of sample proportions

b.

It is known that the distribution of the sample proportions is approximately normal.

The shape of the normal distribution is a bell shape.

Thus, the distribution of the sample proportions of boys is approximately bell-shaped.