Question

Suppose a geyser has a mean time between eruptions of

75 minutes

.

If the interval of time between the eruptions is normally distributed with standard deviation

19 minutes

​,

answer the following questions.

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

84

​minutes?

The probability that a randomly selected time interval is longer than

84

minutes is approximately

nothing

.

​(Round to four decimal places as​ needed.)

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

10

time intervals between eruptions has a mean longer than

84

​minutes?

The probability that the mean of a random sample of

10

time intervals is more than

84

minutes is approximately

nothing

.

​(Round to four decimal places as​ needed.)

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

19

time intervals between eruptions has a mean longer than

84

​minutes?

The probability that the mean of a random sample of

19

time intervals is more than

84

minutes is approximately

nothing

.

​(Round to four decimal places as​ needed.)

​(d) What effect does increasing the sample size have on the​ probability? Provide an explanation for this result. Choose the correct answer below.

A.

The probability decreases because the variability in the sample mean increases as the sample size increases.

B.

The probability increases because the variability in the sample mean decreases as the sample size increases.

C.

The probability increases because the variability in the sample mean increases as the sample size increases.

D.

The probability decreases because the variability in the sample mean decreases as the sample size increases.

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

19

time intervals between eruptions has a mean longer than

84

​minutes? Choose the best answer below.

A.

The population mean must be less than 75 comma since the probability is so low.

B.

The population mean may be greater than 75.

C.

The population mean is

75

​minutes, and this is an example of a typical sampling.

D.

The population mean cannot be 75 comma since the probability is so low.

Answer 1

Let "X" be the time interval between eruptions

The probability that a randomly selected time interval is longer than 84 minutes is approximately

The probability that the mean of a random sample of 10 time intervals is more than 84 minutes is approximately

The probability that the mean of a random sample of 19 time intervals is more than 84 minutes is approximately

The probability decreases because the variability in the sample mean decreases as the sample size increases.

The population mean may be greater than 75.