3 The numbers of CD players sold in a shop on three consecutive weekends were 7, 6 and 2. It may be assumed that sales of CD players occur randomly and that nobody buys more than one CD player at a time. The number of CD players sold on a randomly chosen weekend is denoted by X. (a) How appropriate is the Poisson distribution as a model for X? [2] Now assume that a Poisson distribution with mean 5 is an appropriate model for X. (b) Find (i) P(X=6), [2] (ii) P(X > 8). [2] The number of integrated sound systems sold in a weekend at the same shop can be assumed to have the distribution Po(7.2). (c) Find the probability that on a randomly chosen weekend the total number of CD players and integrated sound systems sold is between 10 and 15 inclusive. [3] (d) State an assumption needed for your answer to part (c) to be valid. (e) Give a reason why the assumption in part (d) may not be valid in practice. ]