Question

Suppose a geyser has a mean time between eruptions of 82 minutes.

Let the interval of time between the eruptions be normally distributed with standard deviation 23 minutes.

Complete parts ​(a) through ​(e) below.

​(a) What is the probability that a randomly selected time interval between eruptions is longer than 93 ​minutes?The probability that a randomly selected time interval is longer than 93 minutes is approximately _______.

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

​(b) What is the probability that a random sample of 9 time intervals between eruptions has a mean longer than 93 ​minutes?The probability that the mean of a random sample of 9 time intervals is more than 93 minutes is approximately ________.

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

​(c) What is the probability that a random sample of 18 time intervals between eruptions has a mean longer than 93 ​minutes?The probability that the mean of a random sample of 18 time intervals is more than 93 minutes is approximately ________.

​(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. Fill in the blanks below.

If the population mean is less than 93 ​minutes, then the probability that the sample mean of the time between eruptions is greater than 93 minutes _________because the variability in the sample mean _________ as the sample size _______.

​(e) What might you conclude if a random sample of 18 time intervals between eruptions has a mean longer than 93 ​minutes? Select all that apply.

A.The population mean must be more than 82​, since the probability is so low.

B.The population mean may be greater than 82.

C.The population mean cannot be 82​, since the probability is so low.

D.The population mean must be less than 82​, since the probability is so low.

E.The population mean is 82​, and this is just a rare sampling.

F.The population mean is 82​, and this is an example of a typical sampling result.

G.The population mean may be less than 82

Answer 1