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12 September, 17:22

A vending machine automatically pours soft drinks into cups. The amount of soft drink dispensed into a cup is normally distributed with a mean of 7.6oz and standard deviation of 0.4oz.

(a) Estimate the probability that the machine will overflow an 8-ounce cup. (Round your answer to two decimal places.)

(b) Estimate the probability that the machine will not overflow an 8-ounce cup. (Round your answer to two decimal places.)

(c) The machine has just been loaded with 848 cups. How many of these do you expect will overflow when served

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  1. 12 September, 20:57
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    Step-by-step explanation:

    Since the amount of soft drink dispensed into a cup is normally distributed, we would apply the formula for normal distribution which is expressed as

    z = (x - µ) / σ

    Where

    x = amount in ounce of soft drink dispensed into cup.

    µ = mean amount

    σ = standard deviation

    From the information given,

    µ = 7.6oz

    σ = 0.4 oz

    a) The probability that the machine will overflow an 8-ounce cup is expressed as

    P (x > 8) = 1 - P (x ≤ 8)

    For x = 8,

    z = (8 - 7.6) / 0.4 = 1

    Looking at the normal distribution table, the probability corresponding to the z score is 0.84

    P (x ≤ 8) = 1 - 0.84 = 0.16

    b) P (x< 8) = 0.84

    c) when the machine has just been loaded with 848 cups, the number of cups expected to overflow when served is

    0.16 * 848 = 136 cups
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