A manufacturer produces plastic bottles whose capacities are

A manufacturer produces plastic bottles whose capacities are normally distributed with a mean of 600 ml and a standard deviation of 0.1 ml. The return policy of the manufacturer stipulates that defective bottles may be returned if the capacity falls outside the range 600 - L

Solution

Mean = 600 sd = .1

If the percent of bottles returned is 8%, then 4% is below this range and 4% is above this range.

Looking up .04 on the standard normal distribution, this occurs at a Z of -1.75

Changing Z to an x:

X = Z*sd + mean = -1.75*.1 + 600 = 599.825

At the other end, Z = 1.75

X = 1.75*.1 + 600 = 600.175

So the bottles would be between 599.825 and 600.175. So L equals 0.175.

Answer: 0.175