Question 1 (4 marks)

Part a)

A sample of n=16 observations is drawn from a normal population with =1000 and=200.Find the following.

i) P(X>1050)

ii) P(960<X<1050)

Part b)

An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with mean=117cm and standard deviation=5.2cm.

i) Find the probability that one selected subcomponent is longer than120cm.

ii) Find the probability that if four subcomponents are randomly selected, their mean

length exceeds120cm