Suppose a geyser has a mean time between eruptions of 100 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 39 minutes. Complete parts (a) through (e) below. (a) What is the probability that a randomly selected time interval between eruptions is longer than 119 minutes? The probability that a randomly selected time interval is longer than 119 minutes is approximately (Round to four decimal places as needed.) (b) What is the probability that a random sample of 10 time intervals between eruptions has a mean longer than 119 minutes? The probability that the mean of a random sample of 10 time intervals is more than 119 minutes is approximately (Round to four decimal places as needed.) (c) What is the probability that a random sample of 19 time intervals between eruptions has a mean longer than 119 minutes? The probability that the mean of a random sample of 19 time intervals is more than 119 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 119 minutes, then the probability that the sample mean of the time between eruptions is greater than 119 minutes because the variability in the sample mean as the sample size Next Search LONCHOG 7:42 AM 11/26/2022 2 19 144 $12 Port sc delete hervariability in the sample mean as the sample size (e) What might you conclude if a random sample of 19 time intervals between eruptions has a mean longer than 119 minutes? Select all that apply. A. The population mean is 100, and this is just a rare sampling B. The population mean may be greater than 100. C. The population mean may be less than 100. D. The population mean is 100, and this is an example of a typical sampling result. E. The population mean must be more than 100, since the probability is so low. F. The population mean must be less than 100, since the probability is so low. G. The population mean cannot be 100, since the probability is so low. O Search O 11 18 144 12 "Sort sc delete home & 6 8 backspace