A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 235.7-cm and a standard deviation of 2-cm. For shipment, 40 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 235.5-cm and 235.7-cm.
4. For a bundled of 40 rods, find the probability that the average length is between 235.5-cm and 235.7-cm.
5. For part d), is the assumption of normal necessary? NoYes