Suppose a geyser has a mean time between eruptions of 79 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 19 minutes, answer the following questions. (a) What is the probability that a randomly selected time interval between eruptions is longer than 87 minutes? The probability that a randomly selected time interval is longer than 87 minutes is approximately nothing. (Round to four decimal places as needed.) (b) What is the probability that a random sample of 14 time intervals between eruptions has a mean longer than 87 minutes? The probability that the mean of a random sample of 14 time intervals is more than 87 minutes is approximately nothing. (Round to four decimal places as needed.) (c) What is the probability that a random sample of 38 time intervals between eruptions has a mean longer than 87 minutes? The probability that the mean of a random sample of 38 time intervals is more than 87 minutes is approximately nothing. (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. Choose the correct answer below. A. The probability decreases because the variability in the sample mean decreases as the sample size increases. B. The probability increases because the variability in the sample mean decreases as the sample size increases. C. The probability decreases because the variability in the sample mean increases as the sample size increases. D. The probability increases because the variability in the sample mean increases as the sample size increases.