Question

One state lottery has 1,200 prizes of $1; 145 prizes of $10; 25 prizes of $60; 5 prizes of $285; 2 prizes of $1,040; and 1 prize of $2,500. Assume that 27,000 lottery tickets are issued and sold for $1.      

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

Answer 1

Lets draw the table

x	1	10	60	285	1040	2500
Frequency	1200	145	25	5	2	1

as total number of tickets = 27000

P(x=1) = 1200/27000

P(x=10) = 145/27000

P(x = 60) = 25/27000

P(x=285) = 5/27000

P(x=1040) = 2/27000

P(x=2500) = 1/27000

Variance = E(x²) - (E(x))²

= {1²*1200/27000 + 10²*145/27000 + 60²*25/27000 + 285²*5/27000 + 1040²*2/27000 + 2500²*1/27000} - {1*1200/27000 + 10*145/27000 + 60*25/27000 + 285*5/27000 + 1040*2/27000 + 2500*1/27000}²

= 330.56 - 0.376²

Thus, Variance = 330.42

Standard deviation = sqrt(Variance) = sqrt(330.42) = $18.18