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 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