You pick a card from a deck.If you get a face card,you win $15.If you get an ace,you win $20 plus an extra $40 for the ace of hearts.For any other card you win nothing.Find the standard deviation of the amount you will win.
A)$10.53
B)$9.69
C)$11.59
D)$110.94
E)$122.09

Question

Quizplus · Accepted Answer

The standard deviation is $10.53. This is because the probability of getting a face card is 3/13, the probability of getting an ace is 1/13, and the probability of getting any other card is 9/13. The expected value of the amount you will win is $15 * 3/13 + $20 * 1/13 + $40 * 1/52 = $10.53. The variance of the amount you will win is $15^2 * 3/13 + $20^2 * 1/13 + $40^2 * 1/52 - $10.53^2 = $111.23. The standard deviation is the square root of the variance, which is $10.53.

You Pick a Card from a Deck