MTH105 Project #2 M&M Version A-1 - CW
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Eastern Gateway Community College *
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Course
105
Subject
Mathematics
Date
Feb 20, 2024
Type
Pages
4
Uploaded by BrigadierBookOwl39
M&M Distribution(A)
MTH105 Project NAME _____________________________________________________________
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 10 blue
Qty 8 orange
Qty 4 yellow
Qty 3 green
Qty 5 brown
Qty 3 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
Orange
Yellow
Green
Brown
Red
1
8/33= .242
10/33= .303
4/33= .121
3/33= .091
5/33= .152
3/33= .091
Cherokee Williams
3.
Suppose the entire class put all the M&Ms together on the table and following occurred:
Qty 42 blue
Qty 45 orange
Qty 33 yellow
Qty 25 green
Qty 10 brown
Qty 22 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
Orange
Yellow
Green
Brown
Red
5.
What conclusions can you draw from the data gathered from one small bag compared to several small bags of M&Ms?
2
42/177= .237
45/177= .254
33/177= .186
25/177= .141
10/177= .056
22/177= .124
It is very hard to guess at how many of every color of M&Ms that is in each bag. Due to the information provided in the study all bags can carry a different amount of each color. Also the M&M's are not packaged with the same amount of every color.
Total: 177 M&M's
6.
A 5-pound bulk bag of M&Ms holds approximately 2900 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
Color
Approximate number of M&Ms
Blue
Orange
Yellow
Green
Brown
Red
7.
A bag of M&Ms is dumped on the table and you count 82 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
3
2900*0.237= 687
2900*0.254= 737
2900*0.186= 539
2900*0.141= 409
2900*0.056= 162
2900*0.124= 360
The blue M&Ms equaled .237 or take .237 and multiply by 100 to get the percentage. 0.237*100 = 23.7% were blue M&Ms. To find the amount of M&Ms in the entire bag you would take 82/0.237 = 345.99 rounded to the nearest M&M would equal 346 M&Ms in the entire bag. Work Check 346*23.7% = 82.002 round to the nearest M&M would equal 82 blue M&Ms
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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?
9.
What are some of the reasons why our bags would differ from the expected distribution? 10.
Why would Mars not put equal amounts of each color in every bag?
4
A reason why our bags differed from the expected distribution is due to the M&Ms are not being counted out in color and split up to meet the expected percentage per bag. This could cause production of M&Ms to decrease or the cost would go up due to hiring more people to count out the M&Ms. I don't feel that from the studies completed that there are very many bags of M&Ms that contain the exact amount of each color.
This idea may add additonal cost to production. Due to more man power being needed to operate the manchies. Also this could close down production due to additonal,
quality and other testing that may now be required. The estimated percentage that Mars claims versus the result from the entire class,Orange was very close to the 25%, Blue was slightly under the 25% but not by far,Yellow was a good bit past the 12.5%, Green was also over a good amount of the 12.5%, Brown was well below the claimed 12.5% and Red was very close to the 12.5%.