Question

One state lottery has 1,100 prizes of $1; 105 prizes of $10; 20 prizes of $60; 5 prizes of $350; 2 prizes of $1,030; and 1 prize of $2,500. Assume that 29,000 lottery tickets are issued and sold for $1.

1) What is the lottery's standard deviation of profit per ticket?

2). What is the lottery's standard deviation of profit per ticket?

Answer 1

Answer:

To determine the lottery's standard deviation of profit per ticket

Expected revenue of ticket = (Pi*Xi)

= (1100 / 29000)*1 + (105/29000)*10 + (20 / 29000)*60 + (5 / 29000)*350 + (2 / 29000)*1030 + (1/29000)*2500

= 0.03793 + 0.03621 + 0.041379 + 0.060345 + 0.0710354 + 0.08621

= 0.333109

Expected revenue of ticket = 0.33311

Expected profit per ticket = Expected revenue per ticket - ticket price

= 0.33311 - 1

Expected profit per ticket = - 0.6669

Here the negative sign indicates that the loss as ticket price is more than the expected return from ticket