Question

7. Imagine you are in a game show. There are 10 prizes hidden on a game board with 100 spaces. One prize is worth $50, three are worth $20, and another six are worth $10. You have to pay $5 to the host if your choice is not correct. Let the random variable x be the winning.

1. Complete the following probability distribution. (Show the probability in fraction format and explain your work)

x	P(x)
-$5
$10
$20
$50

2. What is your expected winning or loss in this game? Be specific in your answer whether it’s winning or loss. (Show work and round the answer to two decimal places)

3.   What is the standard deviation of the probability distribution? (Show work and round the answer to two decimal places)

Answer 1

The probability distribution of X winning amount

X P( X )

-$5 90/100

$10 6/100

$20 3/100

$50 1/100

a) expected winning or loss

E( X ) = X * P( X )

= (-5)*(90/100) + 10*(6/100) + 20*(3/100) + 50*(1/100)

E( X) = -4.5 + 0.6 + 0.6 + 0.5 = -2.80

Expected loss = $ 2.80

b) standard deviation = sqrt [ E(X^{​​​​​2}) - (E( X))²]

E( X^{​​​​​​2}) = 25*(90/100) + 100*(6/100) + 400*(3/100) +2500*(1/100) = 65.5

Standard deviation = sqrt [ 65.5 - 2.80²]

Standard deviation = 7.59