In the questions below, determine the percentage error. Show your work on all pr
ID: 87664 • Letter: I
Question
In the questions below, determine the percentage error. 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 money he is holding within 5% error he can have the money. The son guesses that he is holding 81 cents. The dad opens his hand and displays 90 cents. Did the son guess close enough to receive the money from his father?
A science teacher tells her class that their final project requires the 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?
A locomotive 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 it actually took them 3.26 hours. The train company prides itself on always having its trains to the station within a 3% error of the expected time. Will the train company live up to its reputation on this trip?
In the questions below, determine the percentage error. 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 money he is holding within 5% error he can have the money. The son guesses that he is holding 81 cents. The dad opens his hand and displays 90 cents. Did the son guess close enough to receive the money from his father?
A science teacher tells her class that their final project requires the 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?
A locomotive 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 it actually took them 3.26 hours. The train company prides itself on always having its trains to the station within a 3% error of the expected time. Will the train company live up to its reputation on this trip?
A coach tells his little league players that hitting a 0.275 batting average, within 7% percentage error, means that they had a really great season. Seven year old Tommy ended the season hitting a 0.258 batting average. According to his coach, did he have a great season?
Explanation / Answer
Answer 1: No, the son did not guess the amount close enough to receive money from his father. (As explained below)
Amount of money held by father = 90 cents
5% error in guessing the amount right = 90 x 0.05 = 4.5 cents
So, the permissible limits to deem the guess right = 90 +/- 4.5 i.e either less than 94.5 cents or more than 85.5 cents
Son guessed it 81 cents and that was less than the permissible error limits.
Answer 2: Yes, Jennifer and Johnny will pass their final project. (As explained below)
Actual velocity of the car = 34.15 m/s
2.5% error in the correct velocity = 34.15 x 0.025 = 0.85375 m/s
So, the permissible limits for correct velocity = 34.15 +/- 0.85375 i.e either less than 35.00375 m/s or more than 33.29626 m/s
Jennifer and Johnny guessed the velocity to be 34.87 m/s and that was within permissible limits.
Answer 3: Yes, company lived upto its expectation. (As explained below)
Expected time for trip = 3.15 hours
3% error in expected time = 3.15 x 0.03 = 0.0945 hours
So, the permissible limits for time taken of trip = 3.15 +/- 0.0945 i.e either less than 3.2445 hours or more than 3.0555 hours
The time taken for the trip was 3.26 hours and that was within the permissible limits.
Answer 4: Yes, according to his coach Tommy did have a great season. (As explained below)
Expected batting average = 0.275
7% error in expected average = 0.275 x 0.07 = 0.01925
So, the permissible limits for the batting average = 0.275 +/- 0.01925 i.e either less than 0.29425 or more than 0.25575.
Tommy's batting average was 0.258 and that was within permissible limits.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.