Three out of 200 machine parts were found to be defective.
About how many parts would be expected to be defective out of 2500 parts?
2500(3/200) = ?
To find the expected number of defective parts out of 2500, we can use proportions and ratios.
First, we need to find the proportion of defective parts in the sample of 200.
The proportion of defective parts in the sample is calculated by dividing the number of defective parts by the total number of parts in the sample:
Proportion of defective parts in the sample = (Number of defective parts) / (Total number of parts)
In this case, the number of defective parts is 3, and the total number of parts is 200.
Proportion of defective parts in the sample = 3 / 200
Now, we need to use this proportion to estimate the number of defective parts out of 2500 using ratios.
We set up a ratio comparing the number of defective parts to the total number of parts in the sample as follows:
(Number of defective parts in the sample) / (Total number of parts in the sample) = (Number of defective parts in the population) / (Total number of parts in the population)
We can now substitute the known values:
3 / 200 = (Number of defective parts in the population) / 2500
We can now solve for the unknown value, which is the number of defective parts in the population:
(Number of defective parts in the population) = (3 / 200) * 2500
Using this formula, we can calculate the estimated number of defective parts:
(Number of defective parts in the population) = (3 / 200) * 2500 ≈ 37.5
Therefore, we can expect approximately 37 or 38 out of 2500 parts to be defective.