Question

In: Math

Suppose a geyser has a mean time between eruptions of 66 minutes. If the interval of...

Suppose a geyser has a mean time between eruptions of 66 minutes. If the interval of time between the eruptions is normally distributed with standard deviation

24 minutes​, answer the following question.

What is the probability that a random sample of 38 time intervals between eruptions has a mean longer than 76 ​minutes?

The probability that the mean of a random sample of 38 time intervals is more than 76 minutes is approximately __________

​(Round to four decimal places as​ needed.)

Solutions

Expert Solution

Solution :

Given that ,

mean = = 66

standard deviation = = 24

n = 38

= = 66 and

= / n = 24 / 38 = 3.8933

P( > 76) = 1 - P( < 76)

= 1 - P(( - ) / < (76 - 66) / 3.8933)

= 1 - P(z < 2.95)

= 1-0.9984 Using standard normal table.

Probability = 0.0016

The probability that the mean of a random sample of 38 time intervals is more than 76 minutes is approximately 0.0016.


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