Geyser has a mean time between eruptions of 95 minutes. If the interval of time

Question

Geyser has a mean time between eruptions of 95 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 19 minutes: A.What is the probability that a random sample of 14 time intervals between eruptions has a mean longer than 103 minutes? B.what is the probability that a random sample of 25 time intervals between eruptions has a mean longer than 103 minutes? Geyser has a mean time between eruptions of 95 minutes. If the interval of time between the eruptions is normally distributed with standard deviation 19 minutes: A.What is the probability that a random sample of 14 time intervals between eruptions has a mean longer than 103 minutes? B.what is the probability that a random sample of 25 time intervals between eruptions has a mean longer than 103 minutes? A.What is the probability that a random sample of 14 time intervals between eruptions has a mean longer than 103 minutes? B.what is the probability that a random sample of 25 time intervals between eruptions has a mean longer than 103 minutes?

Explanation / Answer

a) for sample size of 14 ; std error of mean =std deviaiton/(n)1/2 =19/(14)1/2 =5.078

hence  probability that a random sample of 14 time intervals between eruptions has a mean longer than 103 minutes

=P(X>103)=1-P(X<103)=1-P(Z<(103-95)/5.078)=1-P(Z<1.5754)=1-0.9424 =0.0576

b)

for sample size of 25 ; std error of mean =std deviaiton/(n)1/2 =19/(25)1/2 =3.8

hence  probability that a random sample of 25 time intervals between eruptions has a mean longer than 103 minutes

=P(X>103)=1-P(X<103)=1-P(Z<(103-95)/3.8)=1-P(Z<2.1053)=1-0.9824 =0.0176

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