Thread: Normal Distribution: Z- test

A pharmaceutical company manufactures tubes of a certain skin cream. The tubes have a stated volume on the tubes of 125ml, where the content of the tubes has a Normal distribution with a mean mu and a known standard deviation of 0.6ml. If it is a legal requirement for 95% of all tubes sold to contain at least the stated volume, determine the minimum value that mu can take so that the legal requirement is met, giving your answer to the nearest 0.1ml.

Here is a copy of the Z-table.
Please try to help!! Urgent Assignment

is this all the information you were given in the Q?

Yes, it is.

Originally Posted by daphnewoon

A pharmaceutical company manufactures tubes of a certain skin cream. The tubes have a stated volume on the tubes of 125ml, where the content of the tubes has a Normal distribution with a mean mu and a known standard deviation of 0.6ml. If it is a legal requirement for 95% of all tubes sold to contain at least the stated volume, determine the minimum value that mu can take so that the legal requirement is met, giving your answer to the nearest 0.1ml.

You want to determine $\displaystyle \mu$ so that $\displaystyle z= (125- \mu)/.6$ gives 0.95. What z does your table give?
(A very nice table of the normal distribution is at Standard Normal Distribution Table)

After you have found z from the table, solve $\displaystyle z= (125- \mu)/.6$ for $\displaystyle \mu$.

In the table, the z value for 0.95 is 1.645.

Let me just share with you my way of approach.

I actually did slightly differently.

I used 1.96 = (125- mu)/0.6 as I got mixed up with confidence interval.

Appreciated your help here, HallsofIvy!