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25 August, 22:04

In a manufacturing process, a machine produces bolts that have an average length of 3 inches with a variance of. 03. If we randomly select three bolts from this process, what is the probability the mean length of the bolt is "at most 3.1 inches"

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  1. 25 August, 22:33
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    Answer: 0.8413

    Step-by-step explanation:

    population mean = 3

    population variance = 0.03

    sd (standard deviation) = √0.03

    Let x = sample mean

    x has a mean of 3 and sd of √0.03/√3 = √0.01 = 0.1

    And we can aprox the sample mean distribution using a normal distribution

    Note: this approximation maybe is not so good (n = 3)

    with mean = 3 and sd = 0.1

    z = (x-3) / 0.1 has a standard normal distribution

    P (x<3.1) = P (z< (3.1-3) / 0.1) = P (z<1) = 0.8413
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