Question

A school fundraiser sells scratch off tickets with the following prizes: one prize of $1000, ten prizes of $50, twenty prizes of $25, and five hundred prizes of $1. There are 5000 tickets printed to be sold for $1 each.

1. Fill in the probability distribution table below.

Outcome __________ __________ __________ __________ __________

Probability __________ __________ __________ __________ __________

2. Find the expected value. (The average winning amount.)

3. Find the standard deviation of the winning amount.

4. What is the minimum number of tickets that must be sold for the school to meet its goal of making at least $1000?

Answer 1

1.

$1000 Prize = 1 Ticket

$50 Prize = 10 tickey

$25 prize = 20 ticket

$1 prize = 500 Ticket

Total ticket = 5000

Cost of each ticket = $1

No prize on 5000-531(1+10+20+500) 4469 tickets.

Probability Distribution

Outcome (x)	Probability, P(X=x)
$0	4469/5000
$1	500/5000
$25	20/5000
$50	10/5000
$1000	1/5000

2.

We know that,

E(X) = Σ x P(X = x) = μ

E(X) = 0*4469/5000 + 1*500/5000 + 25*20/5000 + 50*10/5000 + 1000*1/5000

= 1/2

3. Std. Deviation = squareroot(∑x²⋅p(x)−μ^{2) =} √(1038/5−(1/2)²⁾ = √4147/20 = ~14.3997

4. Average winnig amount on each ticket = $0.5

Let the number of min ticket to be sold to meet its goal of making at least $1000 be x, then

Sale-Cost > = 1000

x*1 - x*0.5 >= 1000

0.5x >= 1000

x >= 2000