Question

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
yellow	119	0.232
red	103	0.201
orange	52	0.102
green	43	0.084
blue	43	0.084

(round to three decimal places as needed.)
b. draw a pie chart. choose the correct chart below.
○ a. ◉ b. ○ c. ○ d. pie chart options with percentages
c. construct a bar chart. choose the correct chart below.
◉ a. ○ b. ○ c. bar chart options with relative frequency axes

Explanation:

Part (a)

Step 1: Calculate Total Frequency

First, we find the total number of candies by summing up all the frequencies.
The frequencies are: Brown = 152, Yellow = 119, Red = 103, Orange = 52, Green = 43, Blue = 43.
Total frequency \( n = 152 + 119 + 103 + 52 + 43 + 43 \)
\( n = 152+119 = 271 \); \( 271 + 103 = 374 \); \( 374+52 = 426 \); \( 426 + 43 = 469 \); \( 469+43 = 512 \)

Step 2: Calculate Relative Frequency for Each Color

Relative Frequency for a color is given by \( \text{Relative Frequency} = \frac{\text{Frequency of Color}}{\text{Total Frequency}} \)

• Brown: \( \frac{152}{512} \approx 0.297 \)
• Yellow: \( \frac{119}{512} \approx 0.232 \)
• Red: \( \frac{103}{512} \approx 0.201 \)
• Orange: \( \frac{52}{512} \approx 0.102 \)
• Green: \( \frac{43}{512} \approx 0.084 \)
• Blue: \( \frac{43}{512} \approx 0.084 \)

Part (b)

To determine the correct pie chart, we match the relative frequencies with the percentages in each option. The relative frequencies are: Brown (29.7%), Yellow (23.2%), Red (20.1%), Orange (10.2%), Green (8.4%), Blue (8.4%). Looking at the options, option D has these percentages (29.7%, 23.2%, 20.1%, 10.2%, 8.4%, 8.4%) which match our calculated relative frequencies.

To determine the correct bar chart, we analyze the relative frequencies. The relative frequencies are in the order: Brown (≈0.297), Yellow (≈0.232), Red (≈0.201), Orange (≈0.102), Green (≈0.084), Blue (≈0.084). The bar chart should have the tallest bar for Brown, then Yellow, then Red, then Orange, and then Green and Blue with equal (and shorter) bars. Option A shows this pattern (tallest for Brown, then Yellow, then Red, then shorter for Orange, Green, Blue).

Answer:

D

Part (c)