QUESTION 1 Historical data indicated that the time required to service the conveyor belt at Coca-Cola Amatil's Richlands operations can be modelled as a normal distribution with a standard deviation of 17 minutes. A random sample of 34 services revealed a mean service duration of 105.9 minutes. Determine a 99% confidence interval for the mean service time in minutes. State the upper bound of this interval (in minutes) correct to two decimal places. QUESTION 2 Some quality control experiments require destructive sampling in order to measure some particular characteristic of the product. The number of characters printed before a desktop printer fails has been found to be normally distributed. A sample of 'i 5 desktop printers is selected and the number of characters printed (in millions) before each printer fails is recorded. The mean and standard deviation of the number of characters printed by the desktop printers in this sample are calculated in order to build a 99% confidence interval for the mean. State the positive critical value of the test statistic (z or t), exactly as found from the tables (3 decimal places). QUESTION 3 An interval estimate for the average distance car tyres lasted during their "lifetime" was reported to be 32955 km to 36143 km. This interval estimate was based on a sample of 45 tyres. The variance of the lifetime was determined from previous studies to be 47761921 km squared. What level of confidence can be attributed to this interval estimate? State your answer as a percentage, correct to the nearest whole number. QUESTION 4 Sleep apnoea is a sleep disorder that causes a person to stop breathing momentarily and then awaken briefly. A study of 582 Victorian commercial truck drivers found that 101 of them suffered from sleep apnoea. Use the survey results to estimate, with 90% confidence, the proportion of Victorian 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 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 22 for Herron and 28 for the rival company. These yielded an average and variance for the retail price of Herron's product of 372 cents and 83 cents squared respectively, and 407 cents and 52 cents squared for the rival. Under the usual assumptions, determine a 90% confidence interval for the price difference (use Herron minus rival) stating only the upper limit of the interval in cents (round to the nearest whole number). QUESTION 6 The R# Medical Centre undertook a survey to determine the average waiting time of patients in the surgery before they saw a doctor. From 14 responses, the average and standard deviation of the waiting times was found to be 12.8 and 16.36 minutes, respectively. Assuming the information was collected through a random sample and that the waiting time is approximately normally distributed, calculate a 95% confidence interval for the mean waiting time at the medical centre. State the lower bound (in minutes) correct to 3 decimal places. QUESTION 7 1 point The owner of a coffee shop has found that the amount spent by customers at the shop is normally distributed with a mean of $6.80 and a variance of 1.44 $2. If a random sample of 25 customers is selected, what is the probability that the average amount spent by this sample of customers will be greater than $7.40? 0 0.9938 0 0.0062 0 0.5319 0 0.4681