Question: (15 points) An ice cream parlor sells three sizes of ice cream cones: small , medium and large. The small cone costs $1.60 and is purchased by 45% of the customers; the medium cone costs $2.30 and is purchased by 30% of the customers; and the large cone costs $3.20 which is purchased by the rest of the customers.

Let X = the amount of money spent by a customer buying an ice cream cone.

a) (5 pts) Write out the probability distribution for X.
b) (5 pts) Find the mean and variance of X.
c) (5 pts) If it costs an average of $1.90 to make and serve an ice cream cone (server’s time, cone and ice cream, shop overhead, etc), how much profit does the shop owner expect to make per customer?