Question

Suppose a geyser has a mean time between eruptions of 72 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 23 minutes. Complete parts (a) through (e) below.

(a) What is the probability that a randomly selected time interval between eruptions is longer than 82 minutes? The probability that a randomly selected time interval is longer than 82 minutes is approximately nothing. (Round to four decimal places as needed.)

(b) What is the probability that a random sample of 13 time intervals between eruptions has a mean longer than 82 minutes? The probability that the mean of a random sample of 13 time intervals is more than 82 minutes is approximately nothing. (Round to four decimal places as needed.)

(c) What is the probability that a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes? The probability that the mean of a random sample of 34 time intervals is more than 82 minutes is approximately nothing. (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 82 minutes, then the probability that the sample mean of the time between eruptions is greater than 82 minutes_____ because the variability in the sample mean _______as the sample size____.

_(e) What might you conclude if a random sample of 34 time intervals between eruptions has a mean longer than 82 minutes?

Select all that apply. A. The population mean may be less than 72. B. The population mean must be more than 72 , since the probability is so low. C. The population mean cannot be 72 , since the probability is so low. D. The population mean is 72 , and this is just a rare sampling. E. The population mean may be greater than 72. F. The population mean is 72 , and this is an example of a typical sampling result. G. The population mean must be less than 72 , since the probability is so low.

Answer 1