Question

A grocery chain runs a prize game by giving each customer a ticket that may win a prize when the box is scratched off. Printed on the ticket is a dollar value ($500, $100, $25) or the statement "This ticket is not a winner." Monetary prizes can be redeemed for groceries at the store. Below is the probability distribution of the amount won on a randomly selected ticket. Which of the following are the mean and standard deviation, respectively, of the winnings? * 2 points Captionless Image $156.25 $53.85 $15.00, $2900.00 $15.00, $26.93 $15.00, $53.85 $156.25, $26.93

Answer 1

Answer:

$Mean = \ 15$

$Standard\ Deviation = \ 53.85$

Step-by-step explanation:

Given

See attachment for probability distribution

Required

Determine the mean and the standard deviation

The mean of the distribution is:

$Mean = E(x)$

and

$E(x) = \sum x * P(x)$

So, we have:

$Mean = \ 500 * 0.01 + \ 100 * 0.05 + \ 25 * 0.20 + \ 0 * 0.74$

$Mean = \ 5 + \ 5 + \ 5 + \ 0$

$Mean = \ 15$

So:

$E(x) = 15.00$

The standard deviation of the distribution is:

$S = \sqrt{Var(x)}$

Where:

$Var(x) = E(x^2) - (E(x))^2$

$E(x^2) = \sum x^2 * P(x)$

So, we have:

$E(x^2) = 500^2 * 0.01 + 100^2 * 0.05 + 25^2 * 0.20 +0^2 * 0.74$

$E(x^2) = 2500 + 500 + 125 +0$

$E(x^2) = 3125$

So:

$Var(x) = E(x^2) - (E(x))^2$

Where

$E(x^2) = 3125$

$E(x) = 15.00$

$Var(x) = 3125 - 15^2$

$Var(x) = 3125 - 225$

$Var(x) = 2900$

Recall that:

$S =\sqrt{Var(x)$

$S =\sqrt{2900$

$S =53.85$