A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 250.2 cm and a standard deviation of 1.7 cm. For shipment, 12 steel rods are bundled together....

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 250.2 cm and a standard deviation of 1.7 cm. For shipment, 12 steel rods are bundled together.

Note: Even though our sample size is less than 30, we can use the z score because
1) The population is normally distributed and
2) We know the population standard deviation, sigma.


Find the probability that the average length of a randomly selected bundle of steel rods is greater than 251.7 cm.