7 a. What is an Index number? (1mk) b. State four uses of index Numbers (2mks) c. Explain 4 limitations of index numbers (2mks) d. The Kenya Bureau of statistics has provided the flowing data to estimate the cost of living of several households over a two month period Quantity(Kg) Purchases(sh) Commodi ty July August July August Rice 400 500 12000 16000 Sugar 20 15 2200 1500 Maize 80 100 2000 2800 Beans 90 90 3600 3780 You are required to compute: i) The Laspeyre's index (1mks) ii) The Paasches's index (1mks) iii) The Fisher's ideal index (1mks) iv) Kellys index v) Dorbish and bowley index vi) Marshall-edge worth index8. A large group of students took a test in physics and the final grades with the mode of 68, median of 73 and a standard deviation of 10. If we can approximate the distribution of these grades by a normal distribution, what percent of the students a) scored higher than 80? b) should pass the test (grades260)? c) should fail the test (grades