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. bar chart options with relative frequency axes and color labels

Explanation:

Part (a)

Step 1: Calculate Total Frequency

First, we find the total number of candies by summing up all the frequencies.
\[
152 + 119 + 103 + 52 + 43 + 43 = 512
\]

Step 2: Calculate Relative Frequency for Each Color

Relative Frequency is calculated as \(\frac{\text{Frequency of Color}}{\text{Total Frequency}}\).

• Brown: \(\frac{152}{512} \approx 0.297\) (Wait, the given in the problem is 0.279? Wait, maybe I miscalculated. Wait, let's recalculate: \(152 + 119 = 271\), \(271+103 = 374\), \(374 + 52 = 426\), \(426+43 = 469\), \(469 + 43 = 512\). Then Brown: \(152/512 = 0.296875\approx 0.297\), but the problem has 0.279. Wait, maybe the total is different? Wait, maybe the student's data: let's check the frequencies again. Brown:152, Yellow:119, Red:103, Orange:52, Green:43, Blue:43. Sum: 152+119=271, +103=374, +52=426, +43=469, +43=512. So relative frequency for Brown: 152/512 ≈ 0.297, Yellow:119/512≈0.232, Red:103/512≈0.201, Orange:52/512≈0.102, Green:43/512≈0.084, Blue:43/512≈0.084. Wait, the problem's given relative frequencies: Brown 0.279, maybe a typo? But according to the calculation, the relative frequencies are:

Brown: \(\frac{152}{512} \approx 0.297\) (but problem has 0.279, maybe total is different? Wait, maybe the student's three bags, so maybe the total is 152+119+103+52+43+43 = 512. So the relative frequencies are calculated as frequency divided by 512.

So the relative - frequency distribution is:

Color	Frequency	Relative Frequency
Yellow	119	\(\frac{119}{512}\approx0.232\)
Red	103	\(\frac{103}{512}\approx0.201\)
Orange	52	\(\frac{52}{512}\approx0.102\)
Green	43	\(\frac{43}{512}\approx0.084\)
Blue	43	\(\frac{43}{512}\approx0.084\)

Part (b)

To determine the correct pie chart, we compare the relative frequencies with the percentages in each option.

• 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 Brown:29.7%, Yellow:23.2%, Red:20.1%, Orange:10.2%, Green:8.4%, Blue:8.4%, which matches our calculated relative frequencies (or the problem's given relative frequencies when rounded appropriately).

To determine the correct bar chart, we look at the relative frequencies. The relative frequencies are in the order Brown (highest), Yellow, Red, then Orange, Green, Blue (lowest and equal).

• Option A has the bar heights in the order Brown (tallest), Yellow, Red, then Orange, Green, Blue (shorter and equal), which matches the relative - frequency distribution.

Answer:

D

Part (c)