Suppose a geyser has a mean time between eruptions of

88 minutes.

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

25 minutes.

Complete parts (a) through (e) below.

(a) What is the probability that a randomly selected time interval between eruptions is longer than
100
minutes?

Part 2

The probability that a randomly selected time interval is longer than
100
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
9
time intervals between eruptions has a mean longer than
100
minutes?

Part 4

The probability that the mean of a random sample of
9
time intervals is more than
100
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
23
time intervals between eruptions has a mean longer than
100
minutes?

Part 6

The probability that the mean of a random sample of
23
time intervals is more than
100
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
100
minutes, then the probability that the sample mean of the time between eruptions is greater than
100
minutes

▼

increases

decreases

because the variability in the sample mean

▼

decreases

increases

as the sample size

▼

increases.

decreases.

Part 8

(e) What might you conclude if a random sample of
23
time intervals between eruptions has a mean longer than
100
minutes? Select all that apply.

A.

The population mean is
88,
and this is just a rare sampling.

B.

The population mean cannot be
88,
since the probability is so low.

C.

The population mean may be greater than
88.

D.

The population mean must be more than
88,
since the probability is so low.

E.

The population mean is
88,
and this is an example of a typical sampling result.

F.

The population mean may be less than
88.

G.

The population mean must be less than
88,
since the probability is so low.

Question

Suppose a geyser has a mean time between eruptions of

88 minutes.

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

25 minutes.

Complete parts (a) through (e) below.

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

100

minutes?

Part 2

The probability that a randomly selected time interval is longer than

100

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

9

time intervals between eruptions has a mean longer than

100

minutes?

Part 4

The probability that the mean of a random sample of

9

time intervals is more than

100

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

23

time intervals between eruptions has a mean longer than

100

minutes?

Part 6

The probability that the mean of a random sample of

23

time intervals is more than

100

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

100

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

100

minutes

▼

increases

decreases

because the variability in the sample mean

▼

decreases

increases

as the sample size

▼

increases.

decreases.

Part 8

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

23

time intervals between eruptions has a mean longer than

100

minutes? Select all that apply.

A.

The population mean is

88,

and this is just a rare sampling.

B.

The population mean cannot be

88,

since the probability is so low.

C.

The population mean may be greater than

88.

D.

The population mean must be more than

88,

since the probability is so low.

E.

The population mean is

88,

and this is an example of a typical sampling result.

F.

The population mean may be less than

88.

G.

The population mean must be less than

88,

since the probability is so low.

Accepted Answer

Note : As per answering guidelines I have to answer only three subparts. Please repost the remaining…

val of time between the eruptions be normally distributed with standard deviation 25 minutes. Complete parts ​(a) through ​(e) below. ​(a) What is the probability that a randomly selected time interval between eruptions is longer than 100 ​minutes?

Part 2

Part 3

Part 4

Part 5

Part 6

Part 7

Part 8

val of time between the eruptions be normally distributed with standard deviation 25 minutes. Complete parts (a) through (e) below. (a) What is the probability that a randomly selected time interval between eruptions is longer than 100 minutes?