The number of nails of a given length is normally distributed with a mean a length of 5 in. and a standard deviation of 0.03 in. In a bag containing 120 nails, how many nails are between 4.97 in. long and 5.03 in. long? ut 57 nails out 60 nails out 82 nail

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The number of nails of a given length is normally distributed with a mean a length of 5 in. and a
standard deviation of 0.03 in. In a bag containing 120 nails, how many nails are between 4.97
in. long and 5.03 in. long?
ut 57 nails
out 60 nails
out 82 nail
by

1 Answer

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82 nails

Step-by-step explanation:

4.97 and 5.03 are both one standard deviation from the mean...

z scores . 8413 and .1587

.8413 - .1587 = .6826 or 68.26 % of the nails are in this range

68.26 % * 120 = ~82 nails
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