A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 266.8-cm and a standard deviation of 1.1-cm. For shipment, 39 steel rods are bundled together. Round all answers to four decimal places if necessary.
a. What is the distribution of X? X ~ N(266.8, 1.1)
b. What is the distribution of x̄? x̄ ~ N(266.8, 0.1761)
c. For a single randomly selected steel rod, find the probability that the length is between 266.9-cm and 267.2-cm.
d. For a bundled of 39 rods, find the probability that the average length is between 266.9-cm and 267.2-cm.
e. For part d), is the assumption of normal necessary?
No