FOUR (20 marks) a) A company manufactures an average of 400,000 tires annually. On average 2% of tires were manufactured with a defect. A random sample of 500 tires were selected for quality control check. (i) Calculate the mean and standard deviation of the defective tires in this sample (4 Marks) (ii) What is the probability that less than 8 tires will be defective in this sample? (2 marks) (iii)What is the probability that more than 15 tires will have some sort of defect? (2 Marks) (iv) What is the probability that the number of defective tires will be between 7 and 14? b) Rose owns shares in three companies A B C as shown in the table below (3 Marks) mpany Price in 2000 Quantity in 2000 Price In 2021 Quantity in 2021 15 4 23 5 30 2.5 40 2 50 3 60 9 g2000 as the base year, calculate (to 1 decimal point) (i) Laspeyres Index (ii) Paasche Index (iii)Fisher' Index (3marks) (3marks) (3marks) EDCITY