The number of nails of a given length is normally distributed with a mean length of 5.00 in. and a standard deviation of 0.03 in. find the number of nails in a bag of 120 that are between 4.97 and 5.03 in. long.

4.97 is 1 standard deviation below the mean, since 5.00 - 0.03 = 4.97. Similarly, 5.03 is 1 standard deviation above the mean. The 68-95-99.7 rule (sometimes called "empirical rule") says that approximately 68% of any normally distributed population lies within 1 standard deviation of the mean, so

So out of 120 nails, we can expect nails to be within the prescribed length.

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