Bob spends all his free time working to save money for prom. One of his jobs is working at a national coffee chain. Customers earn stars for each purchase which can be redeemed for rewards. There is a holiday promotion where a customer earns a random amount of bonus stars with each purchase. There is a 5% chance of earning 20 stars, a 18% chance of earning 10 stars, a 27% chance of earning 4 stars, and the rest of the time, the customer does not earn any bonus stars. Let S = the number of bonus stars earned by a customer on a single visit. 1. Give the probability distribution of S. You may draw a table.

2. What is the probability that a customer will win fewer than 5 bonus stars?

3. Find the mean of S. Show your equation. Interpret in context.

4. Find the standard deviation of S. Show your equation. Interpret in context.

5. Suppose the coffee chain is feeling extra generous and decides to add triple the number of bonus stars foreach customer purchase. How will the mean and standard deviation of S change?