Suppose a geyser has a mean time between eruptions of 85 minutes. Let the interv

Question

Suppose a geyser has a mean time between eruptions of 85 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 24 minutes. Complete parts (a) through (e) below. (a) What is the probability that a randomly selected time interval between eruptions is longer than 97 minutes? The probability that a randomly selected time interval is longer than 97 minutes is approximately ____. (Round to four decimal places as needed.) (b) What is the probability that a random sample of 6 time intervals between eruptions has a mean longer than 97 minutes? The probability that the mean of a random sample of 6 time intervals is more than 97 minutes is approximately ____. (Round to four decimal places as needed.) (c) What is the probability that a random sample of 21 time intervals between eruptions has a mean longer than 97 minutes? The probability that the mean of a random sample of 21 time intervals is more than 97 minutes is approximately _____. (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 97 minutes, then the probability that the sample mean of the time between eruptions is greater than 97 minutes _____ because the variability in the sample mean ____ as the sample size ___ (e) What might you conclude if a random sample of 21 time intervals between eruptions has a mean longer than 97 minutes? Select all that apply. A. The population mean may be greater than 85. B. The population mean must be less than 85, since the probability is so low. C. The population mean must be more than 85, since the probability is so low. D. The population mean may be less than 85. E. The population mean is 85, and this is an example of a typical sampling result. F. The population mean cannot be 85, since the probability is so low. G. The population mean is 85, and this is just a rare sampling.

Explanation / Answer

a)z = (x - u) / s

=97-85/24

=0.5

p(z>0.5) = 0.3085

b)z = (x - u) * sqrt(n) / s

=1.225

p(z>1.225) =0.1103

c)z = (x - u) * sqrt(n) / s

=(97-85)*sqrt(21)/24

=2.291

p(z>2.291)

=0.0110

d)If the population mean is less than 97 minutes, then the probability that the sample mean of the time between eruption is greater than 97 minutes DECREASES because the variability in the sample mean DECREASES as the sample size INCREASES.

e)The population mean must be more than 85, since the probability is so low

The population mean may be greater than 85

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