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28 August, 07:11

The amount of icing on a Cuppie Cake large cupcake follows a Normal distribution, with a mean of 2 ounces and a standard deviation of 0.3 ounce. A random sample of 16 cupcakes is selected every day and measured. What is the probability the mean weight will exceed 2.1 ounces?

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  1. 28 August, 08:04
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    Answer: the probability the mean weight will exceed 2.1 ounces is 0.09

    Step-by-step explanation:

    Let x be the random variable representing the amount of icing on a Cuppie Cake large cupcake. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,

    z = (x - µ) / (σ/√n)

    Where

    x = sample mean

    µ = population mean

    σ = standard deviation

    n = number of samples

    From the information given,

    µ = 2

    σ = 0.3

    n = 16

    x = 2.1

    the probability that the mean weight will exceed 2.1 ounces is expressed as

    P (x ≥ 2.1)

    For x = 2.1

    z = (2.1 - 2) / (0.3/√16) = 1.33

    We would determine the probability for the area above z = 1.33 from the normal distribution table. It would be

    p = 1 - 0.91 = 0.09

    P (x ≥ 2.1) = 0.09
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