The amount of soda a dispensing machine pours into a 12ounce

The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a mean of 12.03 ounces and a standard deviation of .02 ounces. Every can that has more than 12.05 ounces of soda poured into it causes a spill and the can needs to go through a special cleaning process before it can be sold. How much soda would the cans need to hold if the company wanted to limit the percentage that needed to be cleaned because of spillage to 3%?

Solution

NORMSINV (0.03)=1.8807 (ignore the negative sign)

z=1.8807

z=x-mean/sd

1.8807=(x-12.03)/0.02

Solving for x we get

x=12.07