Question

Suppose a geyser has a mean time between eruptions of 71 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 24 minutes. Complete parts ​(a) through ​(e) below.

​(a) What is the probability that a randomly selected time interval between eruptions is longer than 83 ​minutes? (Round to four decimal places as​ needed.) ​

(b) What is the probability that a random sample of 8 time intervals between eruptions has a mean longer than 83 ​minutes? (Round to four decimal places as​ needed.) ​(

c) What is the probability that a random sample of 24 time intervals between eruptions has a mean longer than 83 ​minutes? 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 83 ​minutes, then the probability that the sample mean of the time between eruptions is greater than 83 minutes ___(increases or decreases) because the variability in the sample mean _____(increases or decreases) as the sample size ____(increases or decreases).

​(e) What might you conclude if a random sample of 24 time intervals between eruptions has a mean longer than 83 ​minutes? Select all that apply.

A. The population mean is 71​, and this is an example of a typical sampling result.

B. The population mean is 71​, and this is just a rare sampling.

C. The population mean may be greater than 71.

D. The population mean must be more than 71​, since the probability is so low.

E. The population mean cannot be 71​, since the probability is so low.

F. The population mean must be less than 71​, since the probability is so low.

G. The population mean may be less than 71.

Answer 1