During the holiday season, the Texas lottery has a scratch-off game called "Stocking Stuffer". One dollar is required to play the game and ticket prizes range from $1.00 to $1000.00. The probability of winning each prize is given below.

PRIZE PROBABILITY

$1000 .00002

100 .00020

50 .00090

20 .004000

5 .00800

2 .05000

1 .11000

1. Find the lottery's expected profit per stocking stuffer ticket

2. find the lottery's variance in profit per stocking stuffer ticket

3. find the lottery's standard deviation in profit per Stocking Stuffer ticket.

A) $0.940

B) 0.886

C) $0.941

Step-by-step explanation:

P(X=xᵢ) = pᵢ

P[X=$1000] = 0.00002

P[X=$100] = 0.0002

P[X=$50] = 0.0009

P[X=$20] = 0.004

P[X=$5] = 0.008

P[X=$2] = 0.05

P[X=$1] = 0.11

Expected value is given by

E(X) = Σ xᵢpᵢ

But because we're finding the profit on each ticket now,

E(X) = (1 - (1000 × 0.00002))+ (1 - (100 × 0.0002))+ (1 - (50 × 0.0009))+ (1 - (20 × 0.004))+ (1 - (5 × 0.008))+ (1 - (2 × 0.05))+ (1 - (1 × 0.11)) = $6.585

On the average of per ticket = $6.585/7 = $0.940

b) Variance = sum of deviations/number of tickets

Sum of deviations = (1 - (1000 × 0.00002))² + [1 - (100 × 0.0002))² + (1 - (50 × 0.0009))² + (1 - (20 × 0.004))² + (1 - (5 × 0.008))² + (1 - (2 × 0.05))² + (1 - (1 × 0.11))² = 6.202925

Variance = 6.202925/7 = 0.886

C) Standard deviation = √(variance)

Standard deviation = √(0.8861321429) = $0.941