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 XXXXXXXXXXfourth prizes of $10 (a) Let Y...

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.