Question

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

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

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

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

(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 increases because the variability in the sample mean increases as the sample size increases.

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

C. The probability increases because the variability in the sample mean decreases 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 21 time intervals between eruptions has a mean longer than 107 minutes? Choose the best answer below.

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

B. The population mean must be more than 93, since the probability 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 the probability 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 of a typical sampling.

Answer 1