1. In a large restaurant an average of 2 out of every 5 customers ask for water with their meal. A random sample of 10 independent customers is selected. (a) What is the probability that exactly 6 customers ask for water with their meal? [2] (b) What is the probability that less than 9 customers ask for water with their meal? [3] (c) What is the expected number of customers who ask for water with their meal? [2] (d) What is the variance of the number of customers customers who ask for water with their meal? [2] (e) A second random sample of 20 independent customers is selected. Find the smallest value of a such that P(X > a) > 0.9 where the random variable X represents the number of these customers who ask for water. [3] (f) The manager of the restaurant has also observed that an average of 2 out of every 5 independent customers ask for extra bread with their meal. What is the distribution of the number of customers who ask for bread and water with their meal? Assume that the number of customers asking for bread is independent to the number of customers asking for water. [3]