Question

Suppose a geyser has a mean time between eruptions of 73 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 26 minutes. Complete parts ​(a) through ​(e) below.

​(a) What is the probability that a randomly selected time interval between eruptions is longer than 84 ​minutes? The probability that a randomly selected time interval is longer than 84 minutes is approximately nothing. ​(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 84 ​minutes? The probability that the mean of a random sample of 14 time intervals is more than 84 minutes is approximately nothing. ​(Round to four decimal places as​ needed.) ​

(c) What is the probability that a random sample of 38 time intervals between eruptions has a mean longer than 84 ​minutes? The probability that the mean of a random sample of 38 time intervals is more than 84 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 84 ​minutes, then the probability that the sample mean of the time between eruptions is greater than 84 minutes ▼ decreases increases because the variability in the sample mean ▼ decreases increases as the sample size ▼ decreases. increases. ​

(e) What might you conclude if a random sample of 38 time intervals between eruptions has a mean longer than 84 ​minutes? Select all that apply.

A. The population mean may be greater than 73.

B. The population mean cannot be 73​, since the probability is so low.

C. The population mean may be less than 73.

D. The population mean is 73​, and this is just a rare sampling.

E. The population mean is 73​, and this is an example of a typical sampling result.

F. The population mean must be less than 73​, since the probability is so low.

G. The population mean must be more than 73​, since the probability is so low.

Answer 1

e) A. The population mean may be greater than 73.