Suppose a geyser has a mean time between eruptions of 62minutes. Let the interval of time between the eruptions be normallydistributed with standard deviation 14 minutes. Complete parts ​(a)through ​(e) below. ​(a) What is the probability that a randomlyselected time interval between eruptions is longer than 68​minutes? The probability that a randomly selected time interval islonger than 68 minutes is approximately nothing. ​(Round to fourdecimal places as​ needed.) ​(b) What is the probability that arandom sample of 9 time intervals between eruptions has a meanlonger than 68 ​minutes? The probability that the mean of a randomsample of 9 time intervals is more than 68 minutes is approximatelynothing. ​(Round to four decimal places as​ needed.) ​(c) What isthe probability that a random sample of 34 time intervals betweeneruptions has a mean longer than 68 ​minutes? The probability thatthe mean of a random sample of 34 time intervals is more than 68minutes is approximately nothing. ​(Round to four decimal placesas​ needed.) ​(d) What effect does increasing the sample size haveon the​ probability? Provide an explanation for this result. Fillin the blanks below. If the population mean is less than 68​minutes, then the probability that the sample mean of the timebetween eruptions is greater than 68 minutes ▼ decreases increasesbecause the variability in the sample mean ▼ decreases increases asthe sample size ▼ increases. decreases. ​(e) What might youconclude if a random sample of 34 time intervals between eruptionshas a mean longer than 68 ​minutes? Select all that apply. A. Thepopulation mean is 62​, and this is just a rare sampling. B. Thepopulation mean may be less than 62. C. The population mean cannotbe 62​, since the probability is so low. D. The population mean maybe greater than 62. E. The population mean must be more than 62​,since the probability is so low. F. The population mean is 62​, andthis is an example of a typical sampling result. G. The populationmean must be less than 62​, since the probability is so low. Clickto select your answer(s).
