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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.

User Seiya
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2 Answers

4 votes

About 3 nails is correct on grad point

User Zeusarm
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1 vote
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
User Rui Marques
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