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10 April, 03:56

11. The number of gallons of carbonated soft drink consumed per person annually is normally distributed with mean 47.5 and standard deviation 3.5. Twenty-five people are selected at random. The probability that the average number of gallons of carbonated soft drink they each consume per year is between 45 and 50 gallons is а bout:

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  1. 10 April, 05:42
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    Step-by-step explanation:

    Since the number of gallons of carbonated soft drink consumed per person annually is normally distributed, we would apply the formula for normal distribution which is expressed as

    z = (x - µ) / σ

    Where

    x = number of gallons of carbonated soft drink.

    µ = mean

    σ = standard deviation

    From the information given,

    µ = 47.5

    σ = 3.5

    We want to find the probability that the average number of gallons of carbonated soft drink they each consume per year is between 45 and 50 gallons. It is expressed as

    P (45 x ≤ x ≤ 50)

    For x = 45,

    z = (45 - 47.5) / 3.5 = - 0.71

    Looking at the normal distribution table, the probability corresponding to the z score is 0.2389

    For x = 50,

    z = (50 - 47.5) / 3.5 = 0.71

    Looking at the normal distribution table, the probability corresponding to the z score is 0.758

    Therefore,

    P (45 x ≤ x ≤ 50) = 0.758 - 0.2389

    = 0.5191
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