A manufacturer of flea collars for animals injects the collars with 15 milligrams of a medicine that only acts on fleas. The manufacturer will only sell collars with 14 milligrams and no more than 16 milligrams of medicine. The following list shows the result of sampling 36 collars from an actual production run of 720 collars.
A) Based on this sample, what percent of the collars would be acceptable? Explain how you got your answer.
B) Based on this sample, how many collars would you expect the manufacturer to reject?
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4
1
9
To answer these questions, we need to determine how many collars fall within the acceptable range.
A) To find the percentage of acceptable collars in the sample, we need to count how many of the sampled collars have a medicine content between 14 and 16 milligrams.
From the given list, we can see that out of 36 collars, 31 collars have a medicine content between 14 and 16 milligrams. So, 31 collars out of 36 are acceptable.
To find the percentage of acceptable collars, we can use the formula:
percentage = (number of acceptable collars / total number of collars) * 100
Plug in the values:
percentage = (31 / 36) * 100 ≈ 86.11%
Therefore, based on this sample, approximately 86.11% of the collars would be acceptable.
B) To find how many collars the manufacturer would expect to reject based on this sample, we need to determine the number of collars that do not fall within the acceptable range.
From the given list, we can see that out of 36 collars, 5 collars have a medicine content outside the range of 14 to 16 milligrams. So, 5 collars out of 36 are expected to be rejected.
Therefore, based on this sample, the manufacturer would expect to reject approximately 5 collars.