Question

The volumes of apple juice in cartons are normally distributed with a standard deviation of 120 mL. Find the mean, to the nearest whole number, if 34% of these cartons contain less that 961 mL of juice?

Answer 1

The normal distribution of this problem is shown in the diagram below

We first need to find the z-score of 961ml of juices. The probability of less than 961 is 34% and by using the symmetrical properties, we can read the value of z when the probability is 34%.

If the z-table only give the value to the left, then we need to work with the probability of 66%

On the table, a portability of 66% gives z-score=0.42

Since the value of X=961 is originally on the left of Mean, μ, then the z-score becomes a negative value

Substitute into the standardizing formula

`-z= (961-μ)/(120)`

`-0.42= (961-μ)/(120)`

`-50.4=961-μ`
μ=1011.4 (to the nearest whole number)