Description
Vending Machine: A vending machine dispenses coffee into an eight-ounce cup. The amounts of coffee dispensed into the cup are normally distributed, with a standard deviation of 0.03 ounce. You can allow the cup to overfill 1% of the time. What amount should you set as a the mean amount of coffee to be dispensed?
Explanation & Answer
x = 8, δ = 0.03
x = μ + zδ
μ = x - zδ
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 8 oz should occur only in 1% of the time).
You can look up the z-value for 0.99 in a Standard Normal Distribution table.
z = 2.32
μ = 8-2.32 *0.03 = 7.93
You get a mean of 7.93 oz.
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