Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 214.4-cm and a standard deviation of 0.6-cm. For shipment, 14 steel rods are bundled together. Round all answers to four decimal places if necessary.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. For a single randomly selected steel rod, find the probability that the length is between 214.2-cm and 214.3-cm.
4. For a bundled of 14 rods, find the probability that the average length is between 214.2-cm and 214.3-cm.
5. For part d), is the assumption of normal necessary?

Answer 1