I propose to contract a taxi ﬁrm for a daily journey of 3km. Study of the traﬃc conditions has suggested to me that the variable time of the journey is reasonably described by the following model:

No. of minutes 5 6 7 8 9 10

Probability 0.08 0.13 0.33 0.25 0.14 0.07 .

(a) The contract oﬀered to me by one ﬁrm involves a charge of £1 per km and 30 pence per minute. What is the average cost of a journey? What is the standard deviation of the cost?

(b) If I envisage the contract running for one year (regarded as 300 independent working days), what would I expect to pay in total? What is the standard deviation of the total annual cost? Do you consider the assumption of independence between days reasonable? Explain your answer.

(c) A second ﬁrm oﬀers a contract of £1.5 per km and 10 pence per minute. Which contract will be more advantageous to me in the long run?