Suppose a geyser has a mean time between eruptions of

63 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation

21 minutes. Complete parts(a) through(e)below.

Question content area bottomPart 1

(a)What is the probability that a randomly selected time interval between eruptions is longer than

72 minutes?

Part 2

The probability that a randomly selected time interval is longer than

72 minutes is approximately

enter your response here

.

(Round to four decimal places as needed.)

Part 3

(b) What is the probability that a random sample of

13 time intervals between eruptions has a mean longer than

72 minutes?

Part 4

The probability that the mean of a random sample of

13 time intervals is more than

72 minutes is approximately

enter your response here

.

(Round to four decimal places as needed.)

Part 5

(c) What is the probability that a random sample of

25 time intervals between eruptions has a mean longer than

72 minutes?

Part 6

The probability that the mean of a random sample of

25 time intervals is more than

72 minutes is approximately

enter your response here

.

(Round to four decimal places as needed.)

Part 7

(d)What effect does increasing the sample size have on the probability? Provide an explanation for this result. Fill in the blanks below.

If the population mean is less than

72 minutes, then the probability that the sample mean of the time between eruptions is greater than

72 minutes

decreases

increases

because the variability in the sample mean

decreases

increases

as the sample size

decreases.

increases.

Part 8

(e) What might you conclude if a random sample of

25 time intervals between eruptions has a mean longer than

72 minutes? Select all that apply.