Question

In: Statistics and Probability

The shape of the distribution of the time required to get an oil change at a...

The shape of the distribution of the time required to get an oil change at a 20​-minute ​oil-change facility is unknown.​ However, records indicate that the mean time is 21.4 minutes, and the standard deviation is 4.5 minutes. ​(b) What is the probability that a random sample of n =35 oil changes results in a sample mean time less than 20 ​minutes? The probability is approximately _______. ​(Round to four decimal places as​ needed.)

Solutions

Expert Solution

Here n = 35 ( > 30 ), which is sufficient for use of central limit theorem.

By central limit theorem , sample mean follow normal distribution with mean = = 21.4

and standard deviation =

Here we want to find P( < 20)

Z score corresponding to 20 is as follow:

So we want to find P( Z < -1.84)

From z table we get  P( Z < -1.84) = 0.0329

Look the following image.

So final answer is 0.0329


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