i) A cola-dispensing machine is set to dispense on average 7.00 ounces of cola per cup. The standard deviation is 0.10 ounces. The distribution amounts dispensed follows a normal distribution. a) What is the probability that the machine will dispense between 7.10 and 7'25 ounces of cola? (2 marks) b) What is the probability that the machine will dispense 7'25 ounces of cola or more? (2 marks} c) What is the probability that the machine will dispense between 6.80 and 7'25 ounces of cola? (2 marks) ii) Print Expert, Inc. purchases plastic cups on which to print logos for sporting events, proms, birthdays, and other special occasions. m the owner, received a large shipment this morning. To ensure the quality of the shipment, he selected a random sample of 300 cups. He found 15 to be defective. Develop a 90 and 99 percent condence interval for the proportion defective. (4 marks} i) In the early 2000s interest rates were low so many homeowners renanced their home mortgages. Linda is a mortgage ofcer at Maybank Savings and Loan. Below is the amount renanced for twenty loans she processed last week. The data are reported in thousands of dollars and arranged from smallest to largest. 59.2 59.5 61.6 65.5 66.6 72.9 74.8 77.3 79.2 83.7 85.6 85.8 86.6 87.0 87.1 90.2 93.3 98.6 100.2 100.7 a) Find the mean, median, 1st quartile and 3rd quartile (4 marks) b) Draw a stem and leaf plot of the data using class width of 10 (2 marks) ii) The sales of Lexus automobiles in the Detroit area follow a Poisson distribution with a mean of 3 per day. a) What is the probability that no Lexus is sold on a particular day? (2 marks) b) What is the probability that for ve consecutive days at least one Lexus is sold? (2 marks)