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
[tex]-z= \frac{961-μ}{120} [/tex]
[tex]-0.42= \frac{961-μ}{120} [/tex]
[tex]-50.4=961-μ[/tex]
μ=1011.4 (to the nearest whole number)
