Introduction to statistics
posted by Shamin on .
A vending machine dispenses coffee into an eightounce cup. The amount of coffee dispensed into the cup is normally distributed with a standard deviation of .03 ounce. You can allow the cup to OVERFILL 1% of the time. What amount should you set as the mean amount of coffee to be dispensed?

x=8, δ=0.03
x=μ+zδ
μ=xzδ
You have to find the mean that makes the range of 0oz to 8oz equal to 0.99 or the 99th percentile (because everything above 8oz should occur only in 1% of the time).
You can look up the zvalue for 0.99 in a Standard Normal Distribution table.
z=2.32
μ=82.32*0.03=7.93
You get a mean of 7.93oz.