Answers INMT2 Integrated Math 2 Sem 2 26-27Volume of Cylinders, Cones, and Spheres

Expected Value Answers

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An investor has an opportunity to invest in three companies. She researched each company and collected the information in the table below. Which company would provide the best investment?Probability of Profit and Loss by CompanyCompanyLoss, Probability of LossProbability to Break EvenProfit, Probability of ProfitA$24,000, 16%50%$10,000, 34%B$12,000, 32%40%$21,000, 28%C$6,000, 23%17%$5,000, 60%

company A

company B

company C

All companies have a probability of loss.

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If a raffle has a winning prize of $100 and each ticket costs $5 with a total of 500 tickets sold, which equation would calculate the expected value?

100 (StartFraction 1 Over 500 EndFraction) + (negative 5) (StartFraction 499 Over 500 EndFraction) = E (X)

95 (StartFraction 1 Over 500 EndFraction) + (negative 5) (StartFraction 499 Over 500 EndFraction) = E (X)

(100 minus 5) (StartFraction 1 Over 500 EndFraction) = E (X)

(100) (StartFraction 1 Over 500 EndFraction) = E (X)

A math club is researching a golf tournament fund-raiser. It will cost $1,000 to host the tournament. If it rains, the club will lose the investment. If it is sunny, it is expected that the club will collect $4,500 from the participants. If the chance of rain is 20%, what is the expected value for the tournament?

–$800

–$200

$2,600

$3,400

Two students devised a game called “3 Pennies & 2 Nickels.” Each player will choose to play the pennies or the nickels. In each round, the players will flip all their coins on the table and record how many heads and tails they have. The table below includes the point scheme.Point Values for “3 Pennies & 2 Nickels”Penny PointsNickel PointsAll pennies heads: –2Both nickels heads: –2At least one of each: +3One of each: +5All pennies tails: –2Both nickels tails: –2Alyssa wants to play the game. Choose the statement below that is correct in all aspects.

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.

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

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

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 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

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)

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

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