Integrating Essential Skills

Mathematics Integrating Essential Skills Q3

Question 3 as printed in the Preparing for the ACT — Practice Test 1 booklet — As printed in the official booklet.

Marco designs a spinner wheel that has exactly 4 sections: red, blue, green, and yellow. He wants the spinner wheel to have a 25% chance of landing on each section. He spins the wheel 500 times. The results of the spins are shown in this table. Spinner Number of times wheel the spinner lands section in each section Red 80 Blue 165 Green 130 Yellow 125 Based on the results in this table, one of the following changes would be the best fix. Which one?

A
He should decrease the area of the red section by increasing the area of the blue section.
B
He should increase the area of the red section by decreasing the area of the blue section.
C
He should increase the area of the red section by decreasing the area of any of the other three sections.
D
He should decrease the area of the blue section, and then it does not matter which section’s area is increased.

Correct answer: B

Explanation from ACT Education Corp.

This question also appears in ACT QuizMe official practice questions, which explains every answer choice.

A. Incorrect. Marco wants the spinner wheel to have a $25 %$ chance of landing on each section. For $500$ spins, this means the spinner should land on each section approximately $0.25 (500) = 125$ times. Be careful when reading values from the table. You may have switched the numbers for the red and blue sections.

B. Correct. Marco wants the spinner wheel to have a $25 %$ chance of landing on each section. For $500$ spins, this means the spinner should land on each section approximately $0.25 (500) = 125$ times. The number of times the spinner landed on the green section and the yellow section are both close to this number already, but the number of times the spinner landed on the red section is too small and the number of times the spinner landed on the blue section is too large. Therefore, Marco should increase the area of the red section by decreasing the area of the blue section.

C. Incorrect. You may have correctly noticed that the number of times that the spinner lands in the red section is less than the number of times it lands in green, yellow, or blue, so the red area needs to be increased. However, it does matter which area gets decreased because the number of times the spinner lands on yellow and green areas are already close to the desired value of $25 %$ of $500$ spins, or $0.25 (500) = 125$ .

D. Incorrect. You may have correctly noticed that the number of times that the spinner lands in the blue section is greater than the number of times it lands in green, yellow, or red, so the blue area needs to be decreased. However, it does matter which area gets increased because the number of times the spinner lands on yellow and green areas are already close to the desired value of $25 %$ of $500$ spins, or $0.25 (500) = 125$ .

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