The most famous geyser in the world, Old Faithful in Yellowstone National Park, has a mean time between eruptions of 85 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 21.25 minutes, complete parts (a) through (f). Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) What is the probability that a randomly selected time interval between eruptions is longer than 95 minutes? longer than 95 minutes is approximately The probability that a randomly selected time interval (Round to four decimal places as needed.) (b) What is the probability that a random sample of 7 time intervals between eruptions has a mean longer than 95 minutes? The probability that the mean of a random sample of 7 time intervals is more than 95 minutes is approximately (Round to four decimal places as needed.) (c) What is the probability that a random sample of 29 time intervals between eruptions has a mean longer than 95 minutes? The probobili y that the moon of a candor f 20 time intenrals is more than 95 minutes is annrorimately

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The most famous geyser in the world, Old Faithful in Yellowstone National Park, has a mean time between eruptions of 85 minutes. If the interval of time between the eruptions is normally distributed with standard
deviation 21.25 minutes, complete parts (a) through (f).
Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2).
(a) What is the probability that a randomly selected time interval between eruptions is longer than 95 minutes?
longer than 95 minutes is approximately
The probability that a randomly selected time interval
(Round to four decimal places as needed.)
(b) What is the probability that a random sample of 7 time intervals between eruptions has a mean longer than 95 minutes?
The probability that the mean of a random sample of 7 time intervals is more than 95 minutes is approximately.
(Round to four decimal places as needed.)
(c) What is the probability that a random sample of 29 time intervals between eruptions has a mean longer than 95 minutes?
The probability that the mean of a random sample of 29 time intervals is more than 95 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.
The probability
because the variability in the sample mean
V as the sample size increases.
Transcribed Image Text:The most famous geyser in the world, Old Faithful in Yellowstone National Park, has a mean time between eruptions of 85 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 21.25 minutes, complete parts (a) through (f). Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) What is the probability that a randomly selected time interval between eruptions is longer than 95 minutes? longer than 95 minutes is approximately The probability that a randomly selected time interval (Round to four decimal places as needed.) (b) What is the probability that a random sample of 7 time intervals between eruptions has a mean longer than 95 minutes? The probability that the mean of a random sample of 7 time intervals is more than 95 minutes is approximately. (Round to four decimal places as needed.) (c) What is the probability that a random sample of 29 time intervals between eruptions has a mean longer than 95 minutes? The probability that the mean of a random sample of 29 time intervals is more than 95 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. The probability because the variability in the sample mean V as the sample size increases.
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