Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 124.7-cm and a standard deviation of 1.6-cm. For shipment, 17 steel rods are bundled together.

Find P₈₃, which is the average length separating the smallest 83% bundles from the largest 17% bundles.
P₈₃ = -cm

Please provide a step-by-step!

Answer 1

Given that,

mean = = 124.7 - cm.

standard deviation = = 1.6 - cm.

n = 17

=   = 124.7

= / n = 1.6/ 17 = 0.39

Using standard normal table

P(Z < z) = 83%

P(Z < z ) = 0.83

P(Z < 0.955 ) = 0.83

z = 0.955

Using z-score formula

= z * +

= 0.955 * 0.39 + 124.7

= 125.1

P83 = 125.1 - cm.