Sure, let's break this down step-by-step.
1. Determine the Observed Frequency for Red Candies:
- According to the provided data, the number of red candies Kathy recorded is 120.
- So, the observed frequency for red candies is [tex]\(120\)[/tex].
2. Calculate the Expected Frequency for Red Candies:
- The candy company claims that the distribution for each color is exactly 20%.
- Since the total count of candies in Kathy's sample is 502, we can calculate the expected number of red candies by multiplying the total candies with the expected proportion (20%).
[tex]\[
\text{Expected Frequency for Red} = \text{Total Candies} \times \text{Expected Proportion}
\][/tex]
[tex]\[
\text{Expected Frequency for Red} = 502 \times 0.20 = 100.4
\][/tex]
So, the observed frequency for the red candies is [tex]\(120\)[/tex] and the expected frequency is [tex]\(100.4\)[/tex].
