A manufacturer of hair care products tested a new shampoo on 5,000 people, and 0.3 percent of the participants experienced a moderate allergic response. 15 of the 5,000 individuals experienced a minor allergic response.
<h3>Define percentage.</h3>
The easiest approach to utilizing percentages is to compare two numbers while setting the second amount's base to 100. Consider for a moment that we are interested in the proportion of working women. A percentage (%) is a number that represents how many out of 100 it is and may also be written as a decimal or fraction. To convert a percentage to a fraction, place the percentage's value in the numerator and 100 in the denominator.
Given,
15 of the 5,000 individuals experienced a minor allergic response.
Dividing the percentage of the population that had a minor reaction.
15 ÷ 5000
0.003
Multiplying it by 100 for percentage:
0.003 × 100%
0.3%
0.3% percent of the people had mild allergic reactions.
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All of them?
Or just the ones in the mddle
Find the mean ( average):
105 + 104 + 110 + 112 + 114 + 106 + 108 +109 = 868
Mean = 868 / 8 = 108.5
Standard deviation:
108.5 - 105 = 3.5, 3.5^2 = 12.25
108.5 - 104 = 4, 4^2 = 16
110 - 108.5 = 1.5, 1.5^2 = 2.25
112 - 108.5 = 3.5, 3.5^2 = 12.25
114 - 108.5 = 5.5, 5.5^2 = 30.25
108.5 - 106 = 2.5, 2.5^2 = 6.25
108.5 - 108 = 0.5, 0.5^2 = 0.25
109 - 108.5 = 0.5, 0.5^2 = 0.25
12.25 + 16 +2.25 + 12.25 + 30.25 +6.25+0.25+0.25 = 79.75
79.75/8 = 9.96875, SQRT(9.96875) = 3.1573
Standard Deviation = 3.1573
108.8 +/- 1.96 *(3.1573/sqrt(8) = 110.687 and 106.312
110.687 - 108.5 = 2.19
108.5 - 106.312 = 2.19
Margin of error = +/- 2.19
Answer:
58
Step-by-step explanation:
remainder 2
Answer : No, the new type of letter wouldn't be considered as a success because its response rate (2.71%) is lower than the average response rate which is 4%.
Hope this helps. - M
