A vending machine dispenses coffee into an eight-ounce cup. The amounts of coffee dispensed into...

So,
${\displaystyle x=\text{Ounces of cup}=8}$ 
${\displaystyle \sigma =\text{Standard deviation}=0.03}$ 
One-tenth of one percent (tenth) of the data values in the top 1% are larger than the cutoff threshold and thus ${\displaystyle 100\mathrm{\%}-1\mathrm{\%}=99\mathrm{\%}}$ are less than the cutoff threshold for the data.
The z-score corresponding to an area of 99% or 0.99 or the nearest area will be found using the standard normal table in the appendix.
The value 0.99 in the appendix's standard normal table is the closest to 0.9901, as noted.
The value.9901, which has a z-score of 2.33, is given in the row beginning with 2.3 and the column beginning with.03.
${\displaystyle z=2.33}$ 
The z-score is defined as the value of x divided by the mean and the standard deviation, though, as we also know.
${\displaystyle z=\frac{x-\mu }{\sigma }}$ 
${\displaystyle \mu =x-z\sigma }$ Solve to ${\displaystyle \mu }$ 
${\displaystyle =8-\left(2.33\right)\left(0.03\right)}$ Substitute 
${\displaystyle =7.9301}$ 
As a result, the average volume of coffee to be delivered is 7.9301 ounces, meaning that the 8-ounce cup will typically overflow 1% of the time.