Suppose a geyser has a mean time between eruptions of 7? minutes. Let the Interval ortime between the eruptions be normally distnbuted ll'ltl'l standard deviation 15 minutes. Complete parts la} through to: below. [a] What is the probability thata randomly selected time interval between eruptions is longer than 33 minutes? The probability that a randomly selected time interval is longerthan 33 minutE is approximately (Round to four decimal places as needed.} {b} What is the probability t:hata random sample of12 time intervals between eruptions has a mean longer than 83 minutes? The probability that the mean ofa random sample of 12 time intervals is more than 33 minutes is approximately (Round to four decimal places as needed.} {cl What is the probability that a random sample of 30 time intervals between eruptions has a mean longer than 33 minutE? The probability that the mean ofa random sample of 30 time intervals is more than 33 minutes is approximately (Round in fun! decimal places as needed.} {d} What eect does increasing the samph size have on the probability? Provide an explanation for this result. Fill in the blanb below. If thepopulation mean is lEE than 83 minutes, then the probability that the sample mean of the time between eruptions is greater than 33 minutes Y because the variability in the sample mean V as the sample size [e] What might you conclude il a random sample M30 time intervals between eruptions has a mean longer than 83 minutes? Select all that apply. A. The population mean may be greater than 77. El. The population mean cannot be Tl". sinw the probability isso low. C. The population mean is 77, and this isjust a rare sampling. El. The population mean must be less than 7?, since the probability is so low. E. The population mean is 77, and this isan example ofa typical samplinp result. F The population mean may be less than 7?. G. The population mean must be more than 77. since the probability is so low