Observing that the proportion of blue candies in his bowl appeared to be less than that of the other colors, a student decided to compare the color distribution in randomly chosen bags of the candy to the theoretical distribution reported by the candy company's consumer affairs. For his study, the student bought three bags of the colored candies from local stores and counted the number of each color. The average number of each color in the three bags (rounded to the nearest integer) was distributed as shown to the right. Use this data to complete parts (a) through (c). a. Obtain a relative-frequency distribution. Color Frequency Relative Frequency Brown 157 Yellow 112 Red 104 Orange 56 Green 43 Blue 12
Observing that the proportion of blue candies in his bowl appeared to be less than that of the other colors, a student decided to compare the color distribution in randomly chosen bags of the candy to the theoretical distribution reported by the candy company's consumer affairs. For his study, the student bought three bags of the colored candies from local stores and counted the number of each color. The average number of each color in the three bags (rounded to the nearest integer) was distributed as shown to the right. Use this data to complete parts (a) through (c). a. Obtain a relative-frequency distribution. Color Frequency Relative Frequency Brown 157 Yellow 112 Red 104 Orange 56 Green 43 Blue 12
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![### Comparing Color Distribution in Candy Bags: An Educational Study
#### Problem Statement:
Observing that the proportion of blue candies in his bowl appeared to be less than that of the other colors, a student decided to compare the color distribution in randomly chosen bags of the candy to the theoretical distribution reported by the candy company's consumer affairs. For his study, the student bought three bags of the colored candies from local stores and counted the number of each color. The average number of each color in the three bags (rounded to the nearest integer) was distributed as shown to the right. Use this data to complete parts (a) through (c).
#### Data Summary:
| Color | Frequency |
|---------|-----------|
| Brown | 157 |
| Yellow | 112 |
| Red | 104 |
| Orange | 56 |
| Green | 43 |
| Blue | 43 |
#### Calculation:
1. **Obtain a relative-frequency distribution.**
To calculate the relative frequency for each color, use the following formula:
\[
\text{Relative Frequency} = \frac{\text{Frequency}}{\text{Total Number of Candies}}
\]
First, calculate the total number of candies:
\[
157 + 112 + 104 + 56 + 43 + 43 = 515
\]
Then, calculate the relative frequency for each color:
- Brown:
\[
\frac{157}{515} \approx 0.3058
\]
- Yellow:
\[
\frac{112}{515} \approx 0.2175
\]
- Red:
\[
\frac{104}{515} \approx 0.2029
\]
- Orange:
\[
\frac{56}{515} \approx 0.1087
\]
- Green:
\[
\frac{43}{515} \approx 0.0835
\]
- Blue:
\[
\frac{43}{515} \approx 0.0835
\]
#### Detailed Explanation:
- The column “Color” lists the different colors of the candies.
- The column “Frequency” shows the average number of each color candy in the bags.
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F037cbcb3-2aa5-4bab-884f-8e4c5e3a2621%2Fbe2e2215-f545-4c9b-bb82-af33af6474e6%2F6sljfnb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Comparing Color Distribution in Candy Bags: An Educational Study
#### Problem Statement:
Observing that the proportion of blue candies in his bowl appeared to be less than that of the other colors, a student decided to compare the color distribution in randomly chosen bags of the candy to the theoretical distribution reported by the candy company's consumer affairs. For his study, the student bought three bags of the colored candies from local stores and counted the number of each color. The average number of each color in the three bags (rounded to the nearest integer) was distributed as shown to the right. Use this data to complete parts (a) through (c).
#### Data Summary:
| Color | Frequency |
|---------|-----------|
| Brown | 157 |
| Yellow | 112 |
| Red | 104 |
| Orange | 56 |
| Green | 43 |
| Blue | 43 |
#### Calculation:
1. **Obtain a relative-frequency distribution.**
To calculate the relative frequency for each color, use the following formula:
\[
\text{Relative Frequency} = \frac{\text{Frequency}}{\text{Total Number of Candies}}
\]
First, calculate the total number of candies:
\[
157 + 112 + 104 + 56 + 43 + 43 = 515
\]
Then, calculate the relative frequency for each color:
- Brown:
\[
\frac{157}{515} \approx 0.3058
\]
- Yellow:
\[
\frac{112}{515} \approx 0.2175
\]
- Red:
\[
\frac{104}{515} \approx 0.2029
\]
- Orange:
\[
\frac{56}{515} \approx 0.1087
\]
- Green:
\[
\frac{43}{515} \approx 0.0835
\]
- Blue:
\[
\frac{43}{515} \approx 0.0835
\]
#### Detailed Explanation:
- The column “Color” lists the different colors of the candies.
- The column “Frequency” shows the average number of each color candy in the bags.
-
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