Question

The weekend wait time for customers at the grocery line is normally distributed with mean 20 minutes and standard deviation 7 minutes. In all samples of size 12, what wait time would 10% of those sample means fall below?

how do we know if the proportion is left-tailed or right tailed

Answer 1

Let , , n=12

Now , the sampling distribution of the sample mean is approximately normally distributed with sample mean and sample standard deviation

We have ,

.............(I)

From standard normal distribution table ,

..............(II)

From (I) and (II) , we get

Therefore , the wait time would 10% of those sample means fall below is 17.41

The proportion is left-tailed , because sample mean fall below