Question

One state lottery has 1,100 prizes of $1; 120 prizes of $10; 30 prizes of $50; 5 prizes of $285; 2 prizes of $1,180; and 1 prize of $2,400. Assume that 34,000 lottery tickets are issued and sold for $1. Round to 4 decimal places for the answers

What is the lottery's expected profit per ticket?

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

Answer 1

Let X = amount of prices

So X takes value as 1, 10, 50, 285, 1180, 2400, and 0

total number of tickets = 34000

So we need to find probability of winning of the prices in each category by dividing 34000 to the total number of prices of that category.

So mean( ) and standard deviation ( ) formula of X is as follow:

Let's make table:

From the table we get

so that mean = = 0.2937

But ticket price is = $1

So the net value = 1 - 0.2937 = $0.7063

and standard deviation is 16.3024

Note: Standard deviation does not affect the change of origin.

What is the lottery's expected profit per ticket?

Answer : $0.7063

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

Answer : $16.3024