Suppose a geyser has a mean time between eruptions of 93minutes. If the interval of time between the eruptions is normallydistributed with standard deviation 28 minutes , answer thefollowing questions.

(a) What is the probability that a randomly selected timeinterval between eruptions is longer than 107 minutes?

(b) What is the probability that a random sample of 7 timeintervals between eruptions has a mean longer than 107 minutes?

(c) What is the probability that a random sample of 21 timeintervals between eruptions has a mean longer than 107 minutes?

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

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

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

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

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

(e) What might you conclude if a random sample of 21 timeintervals between eruptions has a mean longer than 107 minutes?Choose the best answer below.

A. The population mean may be greater than 93.The populationmean may be greater than 93.

B. The population mean must be more than 93, since theprobability is so low. The population mean must be more than 93,since the probability is so low.

C. The population mean must be less than 93, since theprobability is so low. The population mean must be less than 93,since the probability is so low.

D. The population mean is 93 minutes, and this is an example ofa typical sampling.