(a) A company is considering changing its starting business hour from 9:00am to 8:30am.The company has 1200 workers, including 450 office and 750 production workers. A census shows that 370 production workers favour the change, and a total of 715 office and production workers favour the change. To further assess worker opinion, the region manager decides to talk with random workers

(i) Construct a contingency table and evaluate what is the probability of a randomly selected worker being

(1) in favour of the change?

(2) against the change and being an office worker?

(ii) A random sample of 10 workers is selected, what is the probability that 2 of them being in favour of the change and are office workers?

(b) Long-distance telephone calls are normally distributed with a mean of 8 minutes and a standard deviation of 2 minutes. Which of the following case is more likely to occur?

(i) An individual value above 11 minutes, or

(ii) A sample mean above 9 minutes in a sample of 25 calls. Explain.