A lottery that sells 150,000 tickets has the following prize structure:
(1) first prize of $50,000
(2) 5 second prizes of $10,000
(3) 25 third prizes of $1000
(4) 1000 fourth prizes of $10
(a) Let Y be the winning amount of a randomly drawn lottery ticket. Describe the probability distribution of Y.
(b) Compute the mean or expected value of the ticket.
(c) If the ticket costs $1.00, is the purchase of the ticket worthwhile? Explain your answer.
(d) Compute the standard deviation of this distribution. Comment on the usefulness of the standard deviation as a measure of dispersion for this distribution.