Please answer all questions Question 3 ()A firm has a large number of employees.

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Question 3 ()A firm has a large number of employees. The distance in miles thay have to travel each day from home to work can be modelled by a continuous random variable S whose cumulative distribution function is given bv Fs (1) 0 Fs (b)-1 where b represent the farthest distance anyone lives from work. A survey suggests that b-5. U (a) Show that k-1.25 (b)Find the median distance travelled to work (c)Find the probability that an employee lives within half a mile of se this parameter value for part (a) to (d) the median (d) Show that, for any value of b greater than 1, the median distance travelled does not exceed 2 (i) In a cafeteria, baked beans are served either in ordinary portions or in children's portions. The quantity given for an ordinary portion is a normal variable with mean 90g and standard deviation 3g and the quantity given for a child's portion is a normal variable with mean 43g and standard deviation 2g What is the probability that Tom, who has two children's portion, is given more than his father, who has an ordinary portion?

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