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The accuracy of an automatic pitching machine is based on the off-line distance that a pitch is from a target at a distance of 30m. ?

The off-line distance is distributed normally with a mean of 0.0m and a standard deviation of 0.05m. 

A machine will not meet safety standards and will be rejected if its off-line distance is greater than 0.15m. Determine what percentage of machines will be rejected.

1 Answer

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  • 1 week ago

    .15m is three times the standard deviation.

    A machine will meet safety standards if its off-line distance is within three standard deviations.  The Empirical Rule gives that a probability of 99.7%.  Thus, the probability that a machine will be rejected is 0.3%.

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