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Question 2 (a) What do you understand by central tendency? Under what conditions is the median more suitable than other measures of central tendency? [4] A drinks machine dispenses coffee into cups. A sign on the machine indicates that each cup contains 50 ml of coffee. The machine actually dispenses a mean amount of 55 ml per cup and 10% of the cup contain less than the amount stated on the sign. Assuming that the amount of coffee dispensed into each cup is normally distributed, find (i) the standard deviation of the amount of coffee dispensed per cup in ml. [4] (ii) the percentage of cups that contain more than 51 ml. [3] Following complaints, the owners of the machine made adjustments. Only 2.5 % of the cups now contain less than 50 ml. The standard deviation of the amount dispensed is reduced to 3 ml. Assuming that the amount of coffee dispensed is still normally distributed, (iii) find the new mean amount of coffee per cup. [4] (c) The lifetimes of a certain brand of battery have a mean of 45 hours and a standard deviation of 18. Find the probability that the mean lifetime of a random of such 50 batteries will be between 40 and 48 hours. [5] Question 3 1. State the conditions under which the binomial distribution is used. Explain by giving two examples. [5] 2. Post boxes in London are randomly spaced out and on average five post boxes are found per square mile. (a) Determine the probability that on a certain square mile there will be