MTH105 Project #2 M&M Version B
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Eastern Gateway Community College *
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Course
105
Subject
Mathematics
Date
Feb 20, 2024
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docx
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Uploaded by DeaconMantisPerson979
M&M Distribution(B)
MTH105 Project NAME _____
Russ
Stansell_________________________________________
Must show calculations/formula for credit. Any answer given with no calculations shown will result in no credit for that answer. 1.
Suppose you open a bag of M&Ms and count the number of M&Ms you have of each color. Suppose there were the following:
Qty 11 blue
Qty 6 orange
Qty 4 yellow Total quantity = 11 + 6 + 4 + 5 + 3 + 5 = 34
Qty 5 green
Qty 3 brown
Qty 5 red
2.
Calculate the proportion of each color (round to 3 decimals) please show calculation and answer in proportion cell of table example 21/57 = .368
Color
Proportion
Blue
32.353%
Orange
17.647%
Yellow
11.765%
Green
14.706%
Brown
8.824%
Red
14.706%
Blue: (11 / 34) x 100 = 32.35% Red: (5 / 34) x 100 = 14.71%
Orange: (6 / 34) x 100 = 17.65% Brown: (3 / 34) x 100 = 8.82%
Yellow: (4 / 34) x 100 = 11.76% Green: (5 / 34) x 100 = 14.71%
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3.
Suppose the entire class put all the M&Ms together on the table and following occurred:
Qty 45 blue
Qty 47 orange
Qty 31 yellow Total count = 45 + 47 + 31 + 28 + 12 + 19 = 182
Qty 28 green
Qty 12 brown
Qty 19 red
4.
For the entire class, calculate the proportion of each color (round to 3 decimals) please show calculation and answer in proportion cell of table example 21/57 = .368
Color
Proportion
Blue
0.247
Orange
0.258
Yellow
0.170
Green
0.154
Brown
0.066
Red
0.104
Blue: 45 / 182 = 0.2473 Green: 28 / 182 = 0.1538 Orange: 47 / 182 = 0.2582 Brown: 12 / 182 = 0.0659
Yellow: 31 / 182 = 0.1703 Red: 19 / 182 = 0.1044 5.
What conclusions can you draw from the data gathered from one small bag compared to several
small bags of M&Ms?
Comparing data from one small bag of M&Ms to several small bags allows for a more representative sample and reliable conclusions about color proportions. By analyzing multiple samples, variability in color proportions can be assessed, providing insights into the range of proportions within the M&M 2
population. Additionally, examining consistency across samples enhances confidence in the reliability and accuracy of the findings about color distribution
6.
A 5-pound bulk bag of M&Ms holds approximately 2775 pieces. How many of each color should we expect to find in the bag based on the results of the proportions from the entire class
? (approximate number of each color to be rounded to the nearest whole M&M) please show calculation and answer in Approximate number of M&Ms cell of table example 2900*0.368 = 1067
Blue: 0.247 x 2775 = 685 Green: 0.154 x 2775 = 427 Brown: 0.066 x 2775 = 183 Orange: 0.258 x 2775 = 716
Red: 0.104 x 2775 = 288 Yellow: 0.170 x 2775 = 471
Color
Approximate number of M&Ms
Blue
685
Orange
716
Yellow
471
Green
427
Brown
183
Red
288
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7.
A bag of M&Ms is dumped on the table and you count 86 blue pieces. Approximately how many
M&Ms do you expect to be in the entire bag based on the proportions of the entire class?
Round to nearest whole M&M
Show calculation and answer (86 blue / 0.247 blue) x 1 = 348.78 rounded up 349
8.
According to Mars, the makers of M&Ms, their factory produces 25% blue, 25% orange, and 12.5% for each of the remaining colors. How do the observed values based on the entire class compare to these? Blue: 24.7% - 25% = -0.3%
Orange: 25.8% - 25% = +0.8%
Yellow: 17% - 12.5% = +4.5%
Green: 15.4% - 12.5% = +2.9%
Brown: 6.6% - 12.5% = -5.9%
Red: 10.4% - 12.5% = -2.1%
9.
What are some of the reasons why our bags would differ from the expected distribution? These differences between the observed values and the proportions provided by Mars indicate that the M&Ms produced in the factory may not perfectly align with the expected proportions. Various factors, such as production variations or sampling discrepancies, can contribute to these differences.
10.
Why would Mars not put equal amounts of each color in every bag?
First, it makes the production process faster and cheaper. Second, having different colors in each bag makes it more fun and interesting for us consumers. Finally, they might change the amounts based on what people like and want to buy more of. So, it's all about making M&Ms efficiently, keeping us interested, and giving us what we want to eat.
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