Suppose a geyser has a mean time between eruptions of 73 minutes. If the interval of time between the eruptions is normally distributed with standard deviation22 minutes, answer the following questions.Click here to view the standard normal distribution table (page 1).Click here to view the standard normal distribution table (page 2).....(a) What is the probability that a randomly selected time interval between eruptions is longer than 83 minutes?The probability that a randomly selected time interval is longer than 83 minutes is approximately |. (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 83 minutes?The probability that the mean of a random sample of 14 time intervals is more than 83 minutes is approximately (Round to four decimal places as needed.)(c) What is the probability that a random sample of 20 time intervals between eruptions has a mean longer than 83 minutes?The probability that the mean of a random sample of 20 time intervals is more than 83 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. Choose the correct answer below.O A. The probability decreases because the variability in the sample mean decreases as the sample size increases.O B. The probability decreases because the variability in the sample mean increases as the sample size increases.OC. The probability increases because the variability in the sample mean decreases as the sample size increases.O D. The probability increases because the variability in the sample mean increases as the sample size increases.(e) What might you conclude if a random sample of 20 time intervals between eruptions has a mean longer than 83 minutes? Choose the best answer below.O A. The population mean is 73 minutes, and this is an example of a typical sampling.O B. The population mean must be more than 73, since the probability is so low.O C. The population mean may be greater than 73.O D. The population mean must be less than 73, since the probability is so low.

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