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An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are independently and normally distributed with a mean of 120 cm and a standard deviation of 4.7 cm.

Find the probability that if 3 are randomly selected, all 3 have lengths that exceed 122 cm.

  • Statistics -

    Use z-score formula:

    z = (x - mean)/sd

    z = (122 - 120)/4.7 = ?

    Once you have the z-score, check a z-table for the probability (keep in mind that you are looking for the probability exceeding 122 cm).

    After you have the probability from the table, use a normal approximation to the binomial distribution.

    mean = np = 3 * p
    sd = √npq = √(3 * p * q)
    Note: p = probability from z-table; q = 1 - p

    Use z-scores again; this time use 3 for x, the mean calculated above, and the standard deviation calculated above.

    Once you have this z-score, determine the probability using a z-table once again.

    I hope this will help get you started.

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