Ask a New Question
Menu

Arturo spun a spinner 100 times, and the results are shown in the following table.



Number
Frequency
1
15
2
20
3
40
4
25


Arturo's friend, Hazel, models Arturo's experiment by drawing a spinner with four sections. All four sections have different sizes, and the number 4 has the largest section.
Is Hazel's model a good model for Arturo's experiment? Why or why not?

Responses

Yes, since 4 has the greatest frequency, it should have the largest section.
.
No, the sections should all be the same size.

No, the number 3 should have the largest section.

Yes, the only requirement is that there are four sections.

1 answer

To determine whether Hazel's model is a good representation of Arturo's experiment, we need to consider the frequencies of the spinner results and how they correlate to the sizes of the sections on the spinner.

The frequencies from Arturo's 100 spins are as follows:

  • Number 1: 15 times
  • Number 2: 20 times
  • Number 3: 40 times
  • Number 4: 25 times

To model these results accurately, the size of each section on Hazel's spinner should be proportional to the frequency of each number.

Here are the proportions based on the total spins (100):

  • Number 1: \( \frac{15}{100} = 0.15 \) (15%)
  • Number 2: \( \frac{20}{100} = 0.20 \) (20%)
  • Number 3: \( \frac{40}{100} = 0.40 \) (40%)
  • Number 4: \( \frac{25}{100} = 0.25 \) (25%)

Given that the number 3 has the highest frequency (40 times), it should have the largest section on the spinner. If Hazel's spinner has the largest section for the number 4 instead, her model would not accurately represent Arturo's results.

Therefore, the best response to the question is:

No, the number 3 should have the largest section.