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Statistics?

The lengths of 3-inch nails manufactured on a machine are normally distributed with a mean of 3.0 inches and a standard deviation of 0.008 inch. The nails that are either shorter than 2.982 inches or longer than 3.018 inches are unusable. What percentage of all the nails produced by this machine are unusable?

Round your answer to 2 decimal places.

1 Answer

Relevance
  • 1 year ago

    Use the following z-table: https://www.ztable.net/

    P(nails are unusable)

    = P(x < 2.982) + P(x > 3.018)

    = P(z < [2.982 - 3]/0.008) + P(z > [3.018 - 3]/0.008)

    = P(z < -2.25) + P(2.25)

    = 2 × P(z < -2.25)

    = 2 × 0.01222

    = 2.44% (to 2 decimal places)

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