A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 223.7-cm and a standard deviation of 2.3-cm. For shipment, 16 steel rods are bundled together. Round all
answers to four decimal places if necessary.
a. What is the distribution of X? X - N( 223.7
2.3
b. What is the distribution of ?- N
c. For a single randomly selected steel rod, find the probability that the length is between 223.1-cm
and 223.9-cm.
d. For a bundled of 16 rods, find the probability that the average length is between 223.1-cm and
223.9 cm.
e. For part d), is the assumption of normal necessary? No Yes