Question

The shape of the distribution of the time required to get an oil change at a 15​-minute oil-change facility is unknown.​ However, records indicate that the mean time is 16.4 minutes and the standard deviation is 3.5 minutes. To compute probabilities regarding the sample mean using the normal​ model, what size sample would be​ required?

Answer 1

Solution:

Given,

= 16.4

= 3.5

Here we don't know whether the population distribution is normal or not. If the population distribution is normal,then the sampling distribution of the sample mean is also normal, whatever the sample size. But here,we don't know about the normality of the population. When the sample is taken from non normal population ,then the sampling distribution of the sample mean is approximately normal if and only if the sample size is large .The sample is supposed to be large when the sample size is greater than or equal to 30.

So, to compute the probabilities regarding the sample mean using the normal model ,the sample size must be minimum 30.

Then , the sampling distribution of the sample mean is approximately normal with

=    

=  /n