In a sample of 78 widgets, 2 were defective. How many defective widgets would you expect in a sample of 468 widgets?
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To determine the expected number of defective widgets in a sample of 468 widgets, you can use a proportion or ratio approach.
Step 1: Calculate the defect rate in the given sample.
In the given sample of 78 widgets, 2 were defective. To calculate the defect rate, divide the number of defective widgets by the total number of widgets in the sample:
Defect rate = (Number of defective widgets / Total number of widgets) * 100
= (2/78) * 100
= 2.56%
Step 2: Apply the defect rate to the new sample.
To find the expected number of defective widgets in a new sample of 468 widgets, multiply the defect rate by the new sample size:
Expected number of defective widgets = (Defect rate / 100) * Total number of widgets in new sample
= (2.56 / 100) * 468
= 11.98
Therefore, you would expect approximately 12 defective widgets in a sample of 468 widgets.