Answers Fall 24 GMS Advanced Algebra Concepts and Connections AStandard 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

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Expected Value Answers

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