Tim Hortons is a chain that first opened in Hamilton, Ontario. The first two stores offered only coffee and doughnuts, but the selection has grown to muffins, cakes, bagels, and the very successful Timbit (a bite-sized doughnut hole). Despite its success and growth, Tim Hortons does not offer free coffee refills. However, suppose the company is exploring a policy to offer free coffee refills, and the number of refills for a randomly selected customer is a random variable with the probability distribution given in the table.

1. [4 marks]Find the mean, variance, and standard deviation for the number of coffee refills.
2. [4 marks]Suppose each refill costs Tim Hortons 37 cents. Find the mean, variance, and standard
3. deviation of the refill cost.
4. [2 marks]Suppose four customers who order a cup of coffee are selected at random. Find the probability that exactly one customer has two refills.