Question 1 The time taken for a fuel pump to fill a car is very crucial in serving customers efficiently. The Fill Quick fuel station is a chain company that makes pumps with a flow rate that takes 1.25 minutes to fill a 70 litre tank with a standard deviation of 0.14 minutes. Assume the time taken is normally distributed. (a) If a random sample of 35 fuel pumps from different Fill Quick fuel stations was taken, calculate the probability that the mean time taken to fill a 70 litre tank is less than 1.20 minutes. State the probability and show all working including the Excel function used and give answers in two decimal places. (b) It is believed the mean value that was stated above was not correct. From the sample that was collected in part (a) the corrected mean was calculated to be 1.27 minutes to fill up a tank with a sample standard deviation calculated to 0.14 minutes. Calculate a 90% confidence interval estimate of the average time taken to fill a 70 litre tank. Show all steps in your calculation and give the lower and upper limits to two decimal places. Maximum file size: 100MB, maximum number of files