Question
Suppose a geyser has a mean time between eruptions of 63 minutes. Let the interval of time between the eruptions be normally distributed with standard
Suppose a geyser has a mean time between eruptions of
63 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation
21 minutes. Complete parts(a) through(e)below.
Question content area bottomPart 1
(a)What is the probability that a randomly selected time interval between eruptions is longer than
72 minutes?
Part 2
The probability that a randomly selected time interval is longer than
72 minutes is approximately
enter your response here
.
(Round to four decimal places as needed.)
Part 3
(b) What is the probability that a random sample of
13 time intervals between eruptions has a mean longer than
72 minutes?
Part 4
The probability that the mean of a random sample of
13 time intervals is more than
72 minutes is approximately
enter your response here
.
(Round to four decimal places as needed.)
Part 5
(c) What is the probability that a random sample of
25 time intervals between eruptions has a mean longer than
72 minutes?
Part 6
The probability that the mean of a random sample of
25 time intervals is more than
72 minutes is approximately
enter your response here
.
(Round to four decimal places as needed.)
Part 7
(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
72 minutes, then the probability that the sample mean of the time between eruptions is greater than
72 minutes
decreases
increases
because the variability in the sample mean
decreases
increases
as the sample size
decreases.
increases.
Part 8
(e) What might you conclude if a random sample of
25 time intervals between eruptions has a mean longer than
72 minutes? Select all that apply.
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