Question Mathematics Q The times taken to assemble a car in a manufacturing plant follow a normal distribution with a mean of 20 hours and a standard deviation of 2 hours. Use this information to answer the following questions. Show your working, including an appropriate diagram.

a. Find the probability that a randomly selected car takes between 21 and 24 hours to assemble. b. Find the probability that the average assembly time for a randomly selected sample of 5 cars manufactured in the plant will be longer than 22 hours. c. 69% of new cars purchased in Australia have automatic transmission. Find the probability that less than 40 new cars from a random sample of 50 have automatic transmission. Question 2 (15 marks)

In 2013, a study of 50 cruise ships was undertaken to investigate the variables which determine the crew size of a cruise ship. For each of the 50 cruise ships, information was recorded on their most recent cruise. Some of the variables recorded on each cruise ship are described below.

Variable Name Variable Description Ship Name of cruise ship Age Age of the cruise ship in years as of 2013

Cabins Number of cabins Passengers Number of passengers on most recent cruise Crew Number of crew on most recent cruise

The following output was constructed from information recorded on the age and the crew size of the 50 cruise ships in the study. Consider this output for parts a. to f. Regression Analysis: Crew versus Age Model Summary

S R-sq R-sq(adj) R-sq(pred) 235.954 49.67% 48.62% 45.38% Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 1301.3 87.2 14.92 0.000 Age -35.74 5.19 -6.88 0.000 1.00

Regression Equation Crew = 1301.3 - 35.74 Age

Question ¬2 continued a. Comment on the relation between the age of a cruise ship and the number of crew employed on the ship b. Did the oldest cruise ship have the largest crew size?