Skateboard sale. A sports store plans to offer two specially priced skateboard models at a sidewalk sale. The basic model will return a profit of £120 and the sports model £150. Past experiences indicate that sales of the basic model will have a mean of 5.4 skateboards with a standard deviation of 1.2, while sales of the sports model will have a mean of 3.2 skateboards with a standard deviation of 0.8.

The cost of setting up for the sidewalk sale is £200.

a) Define random variables, and use them to express the shop’s net profit.

b) What’s the mean of the net profit?

c) What’s the standard deviation of the net profit?

d) Do you need to make any assumptions in calculating the mean? How about the standard deviation?