Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 197.5-cm and a standard deviation of 2-cm. For shipment, 6 steel rods are bundled together.

Find P11, which is the average length separating the smallest 11% bundles from the largest 89% bundles.

P11 =______________ -cm

Enter your answer as a number accurate to 2 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

P( < x) = 0.11

or, P(( - )/() < (x - )/()) = 0.11

or, P(Z < (x - 197.5)/(2/)) = 0.11

or, (x - 197.5)/(2/) = -1.227

or, x = -1.227 * (2/) + 197.5

or, x = 196.50

So P11 = 196.50