Part a) (3 marks) A sample of n=16 observations is drawn from a normal population with =1000 and =200. Find the following. i) P( >1050) ii) P(960< <1050) Part b) (3 marks) 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 =5.2 cm. i) Find the probability that one selected subcomponent is longer than 120cm. ii) Find the probability that if four subcomponents are randomly selected, their mean length exceeds 120cm.

Question 2 Part a) Calculate the statistic, set up the rejection region, draw the sampling distribution and interpret the result, H0: =50 H1: <50 given that: =15, n=100, >