Answers EAP-Algebra Functions and Data Analysis B CRStandard Deviation

Expected Value Answers

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A company makes a $5 profit on each non-faulty product it sells. Approximately 2% of the products manufactured are faulty, with no way to discover which ones are faulty before delivery. If replacement-and-repair costs for the faulty products are $100 each, what is the profit per item?

loss of $15.10

loss of $15

profit of $2.90

profit of $3.00

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The marketing club at school is opening a student store. They randomly survey 50 students about how much money they spend on lunch each day. What is the expected value for a student to spend on lunch each day? Student Lunch SurveyNumber of StudentsDollars Spent on Lunch Each Day2 $101$812$623$58$44$3

$2.59

$5.11

$5.18

$9.07

Scoring Schemes of Multiple-Choice Tests

scheme A

scheme B

scheme C

scheme D

Penny Points

E(penny) = –0.33 and E(nickel) = 0.33, so she should play with the nickels.

E(penny) = 0.5 and E(nickel) = 1.5, so she should play with the nickels.

E(penny) = 1.75 and E(nickel) = 1.5, so she should play with the pennies.

E(penny) = 2.38 and E(nickel) = 2, so she should play with the pennies.

Given the spinner below in which all regions are equal, which of the following point scales would result in a favorable game?

The odd numbered regions will add one point. The even numbered regions lose one point.

Red will add one point. Any other color will lose one point.

A number less than or equal to 3 will add one point.A 4 will lose two points.

Odds will add a point value equal to the number on the space.Evens will lose a point value equal to the number on the space.

Which statement below correctly depicts the expected value of a fair game?

E(X) = 0

E(X) = 1

E(X) > 0

E(X) >1

A cafeteria purchases milk from one of three providers each week, depending on what other items need to be purchased. The probability of shopping at each store and the cost of one gallon of milk are shown in the table below. Probability and Milk Cost by StoreStoreProbability Milk Cost per GallonA30%$3.00B10%$3.50C60%$2.75The cafeteria should budget $

2.88

2.90

3.00

3.08

Johnny is challenged to a single-player game with an expected value of 1. Which statement below is true?

It is a fair game.

It is a favorable game.

It is unfavorable game.

Johnny cannot determine whether the game is fair without knowing the rules.

loss of $15.10

loss of $15

profit of $2.90

profit of $3.00

Joe takes part in math competitions. A particular contest consists of 25 multiple-choice questions, and each question has 5 possible answers. It awards 6 points for each correct answer, 1.5 points for each answer left blank, and 0 points for incorrect answers. Joe is sure of 12 of his answers. He ruled out 2 choices before guessing on 4 of the other questions and randomly guessed on the 9 remaining problems. What is his expected score?

69.2

75.6

90.8

97.2

A trucking company operates in three regions of the country. The table below depicts the probability that each company truck is in the region and the fuel prices per gallon. What amount should the company budget on average for a gallon of fuel across its operations? Round your answer to the nearest cent.Probability and Fuel Cost by RegionRegionProbability in RegionFuel Cost per GallonSoutheast20%$3.10Southwest30%$3.50California50%$4.05

$3.53

$3.55

$3.68

$3.70

Harlene tosses two number cubes. If a sum of 8 or 12 comes up, she gets 9 points. If not, she loses 2 points. What is the expected value of the number of points for one roll?

Negative two-thirds

Negative one-sixth

one-sixth

Two-thirds

Sebastian has researched the following scoring schemes: one that has 5 question choices, one that has 4 question choices, and two that have 3 question choices. Which scoring scheme is the most favorable to the test taker?Scoring Schemes of Multiple-Choice TestsScoring SchemePoints for Correct AnswerPoints for Incorrect AnswerA (5 choices)1B (3 choices)2C (4 choices)1D (3 choices)3

scheme A

scheme B

scheme C

scheme D

$2.59

$5.11

$5.18

$9.07

Two black chips and three red chips are put into a bag. Two points are awarded for each black chip drawn, and one point is lost for each red chip drawn. What is the expected value for each round if there are two draws per round and the chips are replaced after each draw?

–0.08

–0.04

0.2

0.4

Given the spinner below in which all regions are equal, which of the following point scales would result in a favorable game?

The odd numbered regions will add one point. The even numbered regions lose one point.

Red will add one point. Any other color will lose one point.

A number less than or equal to 3 will add one point.A 4 will lose two points.

Odds will add a point value equal to the number on the space.Evens will lose a point value equal to the number on the space.

A business has an opportunity to invest $35,000. If the investment is a success, the business earns a profit of $150,000. Otherwise, the investment will result in a total loss of all monies. If the investment has 0.27 chance of success, which equation correctly models the expected value of this investment?

0.27(150,000) + 0.73(–35,000) = E(X)

150,000 – 0.73(35,000) = E(X)

0.27(150,000 – 35,000) = E(X)

0.27(115,000) + 0.73(–35,000) = E(X)

A charity is holding a raffle to raise money. There is one car worth $30,000 and five $100 gift cards being raffled off. Each ticket costs $20, and there are a total of 5,000 tickets being sold. Which equation correctly depicts the calculation of the expected value for a ticket?

30,000 (StartFraction 1 Over 5,000 EndFraction) + 100 (StartFraction 1 Over 1000 EndFraction) + (negative 20) (StartFraction 2497 Over 2500 EndFraction) = E (X)

29,980 (StartFraction 1 Over 5,000 EndFraction) + 80 (StartFraction 1 Over 1000 EndFraction) + (negative 20) (StartFraction 2497 Over 2500 EndFraction) = E (X)

30,000 (StartFraction 1 Over 5,000 EndFraction) + 100 (StartFraction 1 Over 1000 EndFraction) = E (X)

29,980 (StartFraction 1 Over 5,000 EndFraction) + 80 (StartFraction 1 Over 1000 EndFraction) = E (X)

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