Gabre8nnych
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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

Respuesta :

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=[tex]\frac{(x-{\mu})}{{\sigma}}[/tex].

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

=[tex]P(z>1)[/tex]

=[tex]0.1587[/tex] b(Using the normal probability table)

In a bag of 20 nails, nails having length more than 5.03 inches=[tex]20{\times}0.1587[/tex]=[tex]19.004[/tex]

= about [tex]19[/tex] nails.

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