Question

Suppose a geyser has a mean time between eruptions of 73 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 18 minutes​, answer the following questions. ​

(a) What is the probability that a randomly selected time interval between eruptions is longer than 81 ​minutes? The probability that a randomly selected time interval is longer than 81 minutes is approximately ___ ​

(b) What is the probability that a random sample of 13 time intervals between eruptions has a mean longer than 81 ​minutes? The probability that the mean of a random sample of 13 time intervals is more than 81 minutes is approximately ___

(c) What is the probability that a random sample of 31 time intervals between eruptions has a mean longer than 81 ​minutes? The probability that the mean of a random sample of 31 time intervals is more than 81 minutes is approximately ___

(d) What effect does increasing the sample size have on the​ probability? Provide an explanation for this result. Choose the correct answer below. A. The probability decreases because the variability in the sample mean increases as the sample size increases. B. The probability increases because the variability in the sample mean decreases as the sample size increases. C. The probability decreases because the variability in the sample mean decreases as the sample size increases. D. The probability increases because the variability in the sample mean increases as the sample size increases.

(e) What might you conclude if a random sample of 31 time intervals between eruptions has a mean longer than 81 ​minutes? Choose the best answer below.

A.The population mean is 73 minutes, and this is an example of a typical sampling.

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

C. The population mean may be greater than 73.

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

Answer 1

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