an analysis showed that 0.06% of the t-shirts made by one company were defective. a student says this is 6 out of every 100. what is the students error
0.06 % = 0.06 / 100 = 0.6 / 1000 = 6 / 10000
6 of 10,000 t-shirt is defective.
The student's error lies in misinterpreting percentages. In this case, the student incorrectly assumes that 0.06% is equivalent to 6 out of every 100.
To understand the student's error, we need to clarify the difference between percentages and proportions. In statistics, a percentage refers to the relative amount out of 100, while a proportion refers to the relative amount out of the total.
If 0.06% of the t-shirts made by the company are defective, this means that out of every 100,000 t-shirts (since 0.06% is generally expressed per 100,000), only 60 are defective (0.06% of 100,000 is 60). Therefore, the proportion of defective t-shirts is 60 out of 100,000, not 6 out of every 100 as the student claimed.
The student made the error of assuming that 0.06% directly corresponds to 6 out of every 100, which is not correct. It's important to correctly interpret percentages and understand their relationship to proportions in order to avoid such errors.