A production process for steel rods, used to reinforce concrete, is known to produce rods whose lengths have a variance of 50 centimeters. The production machinery has been set to produce rods with a mean of 500 centimeters in length. These rods are tied into bundles of 64 for shipment to the construction sites.
What is the probability that the average length of a randomly selected bundle is less than 520cm? Also, what is the probability that the average length of a randomly selected rod is less than 520cm.
This is the answer I got, but i don't know if it is correct
P(x<520) => P(Z<520-500/6.25) => P(Z<3.2) => 0.9993