SOLUTION: Suppose a geyser has a mean time between eruptions of 76 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 15 minutes. What

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Question 1147813: Suppose a geyser has a mean time between eruptions of 76 minutes. Let the interval of time between the eruptions be normally distributed with standard deviation 15 minutes.
What is the probability that a random sample of 7 time intervals between eruptions has a mean longer than 83 ​minutes?
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!
First, you want to find the standard deviation of the sample. You do this by taking the standard deviation of the population and dividing it by the square root of the number of items in the sample:

15%2Fsqrt%287%29 = 15/2.6458 = 5.6694

Zscore = %28x+-+mean%29%2FSD+sample

Zscore = %2883+-+76%29%2F5.6694 = 7%2F5.6694 = 1.23

Go to a z-table and look up +1.23. At a z-score of +1.23, the area to the left of the curve is 0.8907. However, we want to find where the mean is LONGER than 83 minutes, so we want to find the area to the RIGHT of the curve. To do this, we subtract 0.8907 from 1. This comes out to 0.1093.

So, there is a 0.1093 probability the mean of the sample is longer than 83 minutes.