A factory wants to produce iron rods of length 100cm. The actual lengths of the rods can

be modeled by a normal distribution with mean u cm and standard derivation 2 cm.

Random samples of 16 rods each are regularly selected. If the 90% conﬁdence interval

for u derived from a sample does not contain 100, some adjustment must be made on the

machine producing the rods. (a) The lengths (in cm) of 16 rods 1n a sample are given as follows: 98. 76 98. 82 98.99 99. 29 99.35 99. 41 9.9 52 99. 93 Decide whether adjustment must be made on the machine. (b) Given that the true mean length of the rods is 100.9825 cm, ﬁnd the probability that

adjustment will be made after a random sample of 16 rods is inspected. Give your

answer correct to 3 decimal places.