Question

EXERCISE 6: PERCENTAGE ERROR Determine the percentage error in each scenario. Show your work on all problems. A dad holds five coins in his hand. He tells his son that if he can guess the amount of 1. money he is holding within 5% error, he can have the money. The son guesses that dad is holding 81 cents. The dad opens his hand and displays 90 cents. Did the son guess close enough to get the money? A science teacher tells her class that their final project requires students to measure a specific variable and determine the velocity of a car with no more than 2.5% error. Jennifer and Johnny work hard and decide the velocity of the car is 34.87 m/s. The teacher informs them that the actual velocity is 34.15 m/s. Will Jennifer and Johnny pass their final project?I A train is on its way from Chicago, IL to Madison, WI. The trip is said to last 3.15 hours. When the train arrives in Madison, the conductor notices the trip took 3.26 hours. The train company prides itself on always having its trains arrive within a 3% error of the expected time. Will the train company live up to its reputation on this trip?

Answer 1

1) Error in guess = 10%

Hence,

the boy is not within the range thus, he will not get the money

2) Error in Calculation = 2.108 %

since the error is less than the allowed error hence, they will pass their final project

3) Error in arrival time = 3.49 %

since, the error in arrival time is more than the allowed range

Hence,

the company will not live upto its expectation

Explanation:

Given:

1) Allowed error = within 5%

Amount guessed = 81 cents

Actual amount = 90 cents

Error in guess =
`\frac{\textup{Actual-guessed}}{\textup{actual}}*100\%`

Error in guess =
`\frac{\textup{90-81}}{\textup{90}}*100\%`

or

Error in guess = 10%

Hence,

the boy is not within the range thus, he will not get the money

2) Allowed error = within 2.5%

Velocity calculated = 34.87 cents

Actual velocity = 34.15 cents

Error in calculation =
`\frac{|\textup{Actual-Calculated}}{\textup{actual}}*100\%`

Error in calculation =
`\frac{|\textup{34.15-34.87}|}{\textup{34.15}}*100\%`

or

Error in Calculation = 2.108 %

since the error is less than the allowed error hence, they will pass their final project

3) Allowed error = within 3%

Noticed arrival time = 3.26 hours

Actual arrival time = 3.15 cents

Error in arrival time =
`\frac{|\textup{Actual-noticed}}{\textup{actual}}*100\%`

Error in arrival time =
`\frac{|\textup{3.15-3.26}|}{\textup{3.15}}*100\%`

or

Error in arrival time = 3.49 %

since, the error in arrival time is more than the allowed range

Hence,

the company will not live upto its expectation