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Introduction to statistics

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A vending machine dispenses coffee into an eight-ounce 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?

  • Introduction to statistics -

    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 8oz 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 7.93oz.

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