The lengths of nails produced in a factory are normally distributed with a mean of 4.63 cm and a standard deviation of 0.06 cm. find the two lengths that separate the top 7% and the bottom 7%

Question

Normally distributed

Answer 1

z-score of length X is (X-m)/s where m=mean and s=SD. We need X so that P(z)=0.07 and 0.93.

z=-1.475 is the value of z for the lower 7% and so 1.475 is the value for the upper 7%.

(X-4.63)/0.06=-1.475 gives 0.0885=4.63-X, X=4.54cm. (X-4.63)=0.0885, X=4.72cm. So the difference is 0.18cm.