14   Question 5 continued (b) Assuming that it is valid to model X and Y as binomial distributions, give two reasons to justify the use of the approximation in part (a). (2) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (c) Give two reasons in context why the assumptions that Tom made may not be justified. (2) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Turn over 15   Question 5 continued Tom charges £4 for a concession ticket, and £6 for a regular ticket. It costs him £200, in total, to run the cinema for the 7pm showing. (d) Assuming that all tickets are sold for both screens, (i) write an expression for the number of regular tickets sold in terms of T (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (ii) find the probability Tom earns at least £2 125 of profit. Note that profit is total income from sales minus costs. (5) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 5 is 16 marks)