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.