Answer ALL the problems. Show a detailed solution for each question. Microsoft Excel not allowed. 1.Sick leave time used by employees of a firm in one month has a normal distribution with a mean of 250 hours and a variance of 900 hours. Find the probability that a. the total sick leave for next month will be less than 180 hours. (5 points) b. the total sick leave for next month will be more than 280 hours. (5 points) c. the total sick leave for next month will be between 200 and 240 hours. (5 points) 2. The data below gives the petrol consumption figures of cars, with the same engine size when driven at different speeds: SPEED X in mph PETROL CONSUMPTION 30 38 62 25 40 35 80 20 70 26 55 34 75 22 a. Draw a scatter plot. (5 points) b. Find the equation of the best fit line. (10 points) c. Determine the coefficient of correlation and interpret. (8 points) d. Estimate the petrol consumption if the speed of the car is 45 mph. (2 points)