(a)

Sample of  American people of ages to are selected.

Observe the bar graph:

Average number of days per week that Americans of  to is days.

Therefore, .

Standard deviation is day.

Find the probability that American people of ages to spent more than days a week

exercising for a randomly sample of people.

Here .

Find .

Standard deviation of a sample mean is .

Substitute and in the formula.

.

Use the -value formula for a sample mean to find the -value for  .

-value formula: .

Substitute , and .

.

Find the probability.

Using score table:

The area for is .

.

Probability that American people of ages to spent more than days a week exercising is .

(b)

Sample of American people of ages to are selected.

Here .

Observe the bar graph:

Average number of days per week that Americans of  to is days.

Therefore, .

Standard deviation is day.

Find the probability that the average time spent exercising is between and days per week.

Find .

Standard deviation of a sample mean is .

Substitute and in the formula.

.

Use the -value formula for a sample mean to find the -value for  and .

Find -value for .

-value formula: .

Substitute , and .

.

Find -value for .

-value formula: .

Substitute , and .

Find the probability.

Using score table:

The area for  is .

The area for is .

Probability that the average time spent exercising is between and days per week is .

(a) Probability that American people of ages to spent more than days a week exercising is .

(b) Probability that the average time spent exercising is between and days per week is .