a) Name two commonly used discrete probability distributions. [2]

Indicate whether each of the following random variables is discrete or continuous: b) the mass of cans coming off a production line c) the number of employees in a company d) the number of households in Gauteng that have solar heating panels e) the distance travelled daily by a courier service truck. [4] 1. Once a week a merchandiser replenishes the stocks of a particular product brand in six stores for which she is responsible. Experience has shown that there is a one-in five chance that a given store will run out of stock before the merchandiser's weekly visit. a) Which probability distribution is appropriate in this problem? Why? b) What is the probability that, on a given weekly round, the merchandiser will find exactly one store out of stock? c) What is the probability that, at most, two stores will be out of stock? d) What is the probability that no stores will be out of stock? e) What is the mean number of stores out of stock each week? Note: Calculate the probabilities in (b)-(d) using the binomial formula. [10]