Algebra II



Algebra II

Expected Value

Name __________________________

Hour ________

1) The Prova Insurance Company offers a homeowner’s fire insurance policy. Their records indicate that during a year the company will pay out the following amounts for claims due to fires:

$100,000.00 with a probability of .0004

$50,000.00 with a probability of .002

$25,000.00 with a probability of .008

$10,000.00 with a probability of .015

$5,000.00 with a probability of .03

$1,000.00 with a probability of .07

What should be the minimum amount the company charges for each fire policy so that the sum of the premiums can be expected to cover the expenses due to claims?

Amsco’s AP Statistics Preparing for the Advanced Placement Examination, James F. Bohan,

Amsco School Publications, INC; © 2006

2) An investment counselor calls with a hot stock tip. He believes that if the economy remains strong, the investment will result in a profit of $50,000.00. If the economy grows at a moderate pace, the investment will result in a profit of $10,000.00. However, if the economy goes into recession, the investment will result in a loss of $50,000.00. You contact an economist who believes there is a 20% probability the economy will remain strong, a 70% probability the economy will grow at a moderate pace and a 10% probability the economy will slip into a recession. What is the expected profit from this investment?

Statistics, Informed Decisions Using Data, Michael Sullivan III, Pearson – Prentice Hall, © 2007

3) Some standardize tests, such as the SAT test, incorporate a penalty for wrong answers. For example, a multiple–choice question with five possible answers will have 1 point awarded for a correct answer, and ¼ deducted for an incorrect answer. Questions left blank are worth 0 points. Find the expected number of points received for a multiple–choice question with five possible answers when a student just guesses.

Statistics, Informed Decisions Using Data, Michael Sullivan III, Pearson – Prentice Hall, © 2007

4) The Michigan Lotto game was a game in which a player has to match 6 of 49 numbers to win the jackpot. What is the expected value for this game?

Match Prize Probability of Winning

6 of 6 $2,000,000.00 [pic]

5 of 6 $2,500.00 [pic]

4 of 6 $100.00

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