Problem

(a) Explain what you understand by the sampling distribution of a statistic.

At Sam’s cafe a standard breakfast consists of 6 breakfast items. Customers can then choose to upgrade to a medium breakfast by adding 1 extra breakfast item or they can upgrade to a large breakfast by adding 2 extra breakfast items. Standard, medium and large breakfasts are sold in the ratio 6 : 3 : 2 respectively. A random sample of 2 customers is taken from customers who have bought a breakfast from Sam’s cafe on a particular day.

(b) Find the sampling distribution for the total number, $T$, of breakfast items bought by these 2 customers. Show your working clearly.

(c) Find $E(T)$

(Total for Question 6 is 10 marks)