Question

1. 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. 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

Explanation:

Step1: Calculate the expected number of times

The spinner is spun \(n = 500\) times. Since each section should have a \(25\%=\frac{1}{4}\) chance of being landed on, the expected number of times for each section is \(E=\frac{1}{4}\times500 = 125\) times.

Step2: Analyze the deviation

• Red: Observed \(O_{red}=80\), deviation \(d_{red}=125 - 80=45\) (needs to increase by 45)
• Blue: Observed \(O_{blue}=165\), deviation \(d_{blue}=165 - 125 = 40\) (needs to decrease by 40)
• Green: Observed \(O_{green}=130\), deviation \(d_{green}=130 - 125=5\)
• Yellow: Observed \(O_{yellow}=125\), deviation \(d_{yellow}=125 - 125 = 0\)

To make the probabilities closer to \(25\%\) for each section, we need to increase the area of the red section (to increase its landing probability) and decrease the area of the blue section (to decrease its landing probability)

Answer:

B. He should increase the area of the red section by decreasing the area of the blue section.