The accompanying graph gives the monthly expenditure (in $) on food for a random sample of households in a certain city.1.1 Obtain the frequency distribution for the data represented by the above graph. (3)1.2 Use the information in 1.1 to determine each of the following quantities.1.2.1 mean (5) 1.2.2 mode (2) 1.2.3 80th percentile. (3)1.3 Calculate the coefficient of variation and comment on the value obtained. (8)QUESTION 2 (22)2.1 The probability that a random sample of 10 invoices of a company contains 2 errors is 0.45 and the probability that the sample contains 3 errors is 0.30. If 200 invoices are chosen randomly from the company's records, estimate the number of invoices that will contain errors. (7) 2.2 A manufacturer of precision tools specifies that the diameter of a circular disc must be 10 cm with a tolerance of 1 cm. The machine produces these discs with diameters that are normally distributed with a standard deviation of 5 mm. If the mean diameter is set to 10 cm, what proportion of discs will be rejected as outside the tolerance limits? Discs with diameters above the upper limit can be reworked to within the specifications, but those that are below the lower limit have to be scrapped. If it is desired that at most 1% output can be scrapped, what should be the setting for the mean? When the mean is so set, what proportion of discs will have to be reworked? If the cost of production of a disc is $10, and the cost of reworking a disc is $2, how much would it cost to have 1000 discs ready for shipping? (15) QUESTION 3 (14)Three different training programs (A, B, C) were tested for their impact on performance on a group of workers at a large company. After 4 months, each worker was rated in terms of job performance. The results are summarized in the accompanying table.Performance A B CNone 20 39 31Moderate 45 89 36Great 35 22 33Investigate fully, at the 5% level of significance, whether or not the data suggest differences in the programs relating to their impact on the performance of the workers.QUESTION 4 (23)A giant retail giant has recorded the quarterly sales volumes (in $m) over the past four years. The sales data is shown in the table below.Quarter Year 1 Year 2 Year 3 Year 4Jan – Mar 55 56 51 62Apr – Jun 60 64 70 75Jul – Sep 96 90 100 103Aug – Dec 72 81 90 83Using the ratio-to-moving average method and linear regression, predict the sales volume for each quarter of year 5. Assume that cyclical and random factors do not contribute significantly to the time series. Show details of all calculations. QUESTION 5 (20)An oil company is considering whether or not to bid for an offshore drilling contract. If they bid, the value would be $600 m with a 65% chance of gaining the contract. The company may set up a new drilling operation or move its already existing operation, which has proved successful to the new site. The probability of success and expected returns (in $m) are as follows: Outcome New Operation Existing Operation Probability Exp. Return Probability Exp. Return Success 0.75 800 0.85 700Failure 0.25 200 0.15 350If the company does not bid or lose the c