Question

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 less than 4.94 in. long.

Answer 1

About 3 nails is correct on grad point

Answer 2

the number of nails in a bag of 120 that are less than 4.94 in. long will be found as follows:
P(x<4.94)=P(z<Z)
Z=(x-μ)/σ
where:
x=4.94 in
μ=5 in
σ=0.03
thus
Z=(4.94-5)/0.03
Z=-2
thus
P(x<4.94)=P(z<-2)=0.0228

Thus the number of nails that are less than 4.94 will be:
0.0228×200=4.56~5 nails