(a) A car company collected data and found that their brake pads lasted for a mean distance of 180 thousand kilometers with a standard deviation of 20 thousand kilometers. The data was found to be normally distributed. The supplier of the brake pads had specified the lifetime of the brake pads to be 150 thousand kilometers. (i) What percentage of brake pads will under perform? 1 Mark (ii) The car company has decided to specify the percentage of brake pads that under perform to 1%. What should the standard deviation need to be to meet this requirement? 1 mark (b) The annual income of car company workers on the production line was found to have a mean of $35,000 and a standard deviation of $6,000. If random samples of 50 production line workers were taken from the production line, calculate the proportion of sample mean annual incomes that would exceed $37,500. 1 mark (c) The number of years of service of 10 car company production line workers varies uniformly between 5 years and 12.5 years. What is the probability that the length of employment for a production line worker is 10 years? 1 mark