A motor home sales department has created three plans for purchasing a new or used motor home for leisure to increase potential sales of its f leet. They estimate that 20%

of the potential customers will choose plan 1, which includes no down payment with a 10-year finance option; 40% will choose plan 2, which includes a 20% down payment with a 7-year finance option; and 40% will choose plan 3, which includes 40% down payment and a 5-year finance option.

a) Find the expected value of the type of down payment potential customers will need to make.

b) Find the standard deviation of the type of down payment potential customers will need to make.