The number of nails of a given length is normally distributed with a mean of 5.00 in. and a standard deviation of 0.03 in. Find the number of nails in a bag of 120 that are in between 49.7 and 5.03 in. long.
A. 20 nails
B. 40 nails
C. 46 nails
D. 82 nails

Question

The number of nails of a given length is normally distributed with a mean of 5.00 in. and a standard deviation of 0.03 in. Find the number of nails in a bag of 120 that are in between 49.7 and 5.03 in. long.
A. 20 nails
B. 40 nails
C. 46 nails
D. 82 nails

anonymous · Answer

it will be 40 nails

kropot72 · Answer

Assuming you question should read ".........in between 4.97 and 5.03 in. long", the given limits are minus and plus one standard deviation of the mean.
The 'empirical rule' states that for all normal distributions approximately 68% of the data points lie within the range plus and minus one standard deviation of the mean.
Therefore in your question the approximate number of nails is found from:
$$\large 120\times0.68=(you\ can\ calculate)\ nails$$
Note: Remember to round your answer to the nearest nail.