Suppose a geyser has a mean time between eruptions of 72 minutes. If the interva

Question

Suppose a geyser has a mean time between eruptions of 72 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 15 minutes?, answer the following questions.?(a) What is the probability that a randomly selected time interval between eruptions is longer than 79 ?minutes? The probability that a randomly selected time interval is longer than 79 minutes is approximately nothing. ?(Round to four decimal places as? needed.) ?(b) What is the probability that a random sample of 8 time intervals between eruptions has a mean longer than 79 ?minutes? The probability that the mean of a random sample of 8 time intervals is more than 79 minutes is approximately nothing. ?(Round to four decimal places as? needed.) ?(c) What is the probability that a random sample of 20 time intervals between eruptions has a mean longer than 79 ?minutes? The probability that the mean of a random sample of 20 time intervals is more than 79 minutes is approximately nothing.

Explanation / Answer

a)

X = N(72,15^2)

Z = (X - mean)/sd = (X - 72)/15

P(X > 79)

=

P (Z>0.47)=0.3192

b)

sd(Xbar) = 15/sqrt(8) = 5.303300

Xbar = N(72 , 15^2/8)

P(Xbar > 79)

=

P (Z>1.32)=0.0934

c)

when n = 20

sd(Xbar) = 15/sqrt(20) = 3.35410196625

P(Xbar > 79)

=

P (Z>2.09)=0.0183

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