Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 93.6-cm and a standard deviation of 1.6-cm. For shipment, 30 steel rods are bundled together.

Find P₃₂, which is the average length separating the smallest 32% bundles from the largest 68% bundles.
P₃₂ =___________ -cm

Enter your answer as a number accurate to 2 decimal place.

Answer 1

Solution,

Given that,

mean = = 93.6 -cm

standard deviation = = 1.6 -cm

n = 30

= = 93.6 -cm

= / n = 1.6 / 30 = 0.29 -cm

Using standard normal table,

P(Z < z) = 32%

= P(Z < z) = 0.32  

= P(Z < -0.47) = 0.32

z = -0.47

Using z-score formula  

= z * +

= -0.47 * 0.29 + 93.6

= 93.46

P32 = 93.46 -cm.