QUESTION 1 Historical data indicated that the time required to service the conveyor belt at CocaCola Amatil's Richlands operations can be modelled as a normal distribution with a standard deviation of 22 minutes. A random sample of 18 services revealed a mean service duration of 82.9 minutes. Determine a 99% confidence interval for the mean service time in minutes. State the upper bound ofthis interval {in minutes} correct to two decimal places. QUESTION 2 A study on highway safety studied the driving habits of individuals. A sample of 74 cars travelling on the highway revealed an average speed of 102 kph with a standard deviation of 12.3 kph. Determine the critical value of the test statistic needed for a 95% confidence interval forthe mean speed of all cars, ifit is known that speed is normally distributed. Give the positive answer of the test statistic {z or t) exactly as found from tables {3 decimal places). QUESTION 5 A sales consultant for Herron Pharmaceuticals wished to confirm that their packet of 24 paracetamol tablets was cheaper at the retail level than their rival product. The sales consultant collected price data from two independent samples, of size 19 for Herron and 26 for the rival company. These yielded an average and variance forthe retail price of Herron's product of 377 cents and 68 cents squared respectively, and 398 cents and 55 cents squared for the rival. Underthe usual assumptions, determine an 80% confidence interval forthe price difference (use Herron minus rival) stating only the lower limit ofthe interval in cents [round to the nearest whole number), QUESTION 6 In order to determine the average weight of large posteit parcels at a post office, a sample of3i parcels was weighed. The average weight was found to be 6.5 kg with a standard deviation of 4.1 kg. Determine a 90% confidence interval for the mean. State the lower limit only (in kg) correct to two decimal places. QUESTION 3 A market research company conducted a telephone survey of 765 Melbourne households to determine the proportion of households seeking to purchase a new car in the next two years. An interval estimate of 0.068 to 0.112 was found. Determine the level of confidence for this interval [answer as percentage to 2 decimal places). QUESTION 4 Sleep apnoea is a sleep disorder that causes a person to stop breathing momentarily and then awaken briefly. A study of 474 Victorian commercial truck drivers found that 98 of them suffered from sleep apnoea. Use the survey results to estimate, with 93% confidence, the proportion ofVictorian commercial truck drivers who suffer from this sleeping disorder. Report the upper bound of the interval only, giving your answer as a percentage to two decimal places. QUESTION 7 Suppose that the duration of trouble-free operation of a new vacuum cleaner is normally distributed with a mean of 550 days and a standard deviation of 100 days. The research department randomly selects 25 customers who bought these vacuum cleaners and records the duration (in days) of trouble-free operation. Which of the following is NOT TRUE for the sample average of number oftrouble-free operation days (_\\ )? C- p (x 600) = P(Z > 2.5) {I} p (x