The most famous geyser in the world, Old Faithful in Yellowstone National Park, has a mean time between eruptions of 85 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 21.25 minute complete parts (a) through (f). c) What is the probability that a random sample of 33 time intervals between eruptions has a mean longer than 94 minutes? The probability that the mean of a random sample of 33 time intervals is more than 94 minutes is approximately 0.0075. 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. f the population mean is less than 94 minutes, then the probability that the sample mean of the time between eruptions is greater than 94 minutes decreases because the variability in the sample mean decreases as the sample size increases. e) What might you conclude if a random sample of 33 time intervals between eruptions has a mean longer than 94 minutes? Select all that apply. The population mean may be greater than 85 minutes. OB. The population mean may be less than 85 minutes. c. The population mean cannot be 85 minutes, since the probability is so low. O D. The population mean is 85 minutes, and this is an example of a typical sampling result. E. The population mean must be more than 85 minutes, since the probability is so low. IF. The population mean must be less than 85 minutes, since the probability is so low. *G. The population mean is 85 minutes, and this is just a rare sampling. () On a certain day, suppose there are 26 time intervals for Old Faithful. Treating these 26 eruptions as a random sample, there is a 0.20 likelihood that the mean length of time between eruptions will exceed what value? The likelihood the mean length of time between eruptions exceeds minutes is 0.20. "Round to one decimal place as needed.)

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