Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 116.4-cm and a standard deviation of 0.8-cm. For shipment, 29 steel rods are bundled together. Find the probability that the average length of a randomly selected bundle of steel rods is less than 116-cm.

Answer 1

Calculate lengths from each of the lengths (116.4 & 0.8), using the well known formula z = (x-μ) / σ.

Look up the Probabilities associated with those two lengths

Subtract the lesser probability from greater of these two probabilities, to get probability 0.8 in the associated interval.