Gabre8nnych
Answered

The number of nails of a given length is normally distributed with a mean length of 5 in. and a standard deviation of 0.03 in. In a bag containing 120 nails, how many nails are more than 5.03 in. long?


a.about 38 nails

b.about 41 nails

c.about 16 nails

d.about 19 nails

Verified Answer :

meerkat18

The length 5.03 inches belonged to the first range of span of standard deviation. The probability of having length below 5.03 is equal to 68%. The proprobability of having length above 5.03 therefore is (100-68)/2 or equal to 16%. 16% of 120 nails given is 19.2 or D. about 19 nails.

boffeemadrid

Answer:

(D) About 19 nails

Step-by-step explanation:

It is given that mean length= 5 inches and the standard deviation =0.03.

In order to standardize x to z, we use the formula=\(\frac{(x-{\mu})}{{\sigma}}\).

Now, probability of nails having length more than 5.03= \(P(x>5.03)=P(z>\frac{(5.03-5)}{0.03})\)

=\(P(z>1)\)

=\(0.1587\) b(Using the normal probability table)

In a bag of 20 nails, nails having length more than 5.03 inches=\(20{\times}0.1587\)=\(19.004\)

= about \(19\) nails.