Question

From 15,000 graphing calculators produced by a manufacturer, an inspector selects a random sample of 450 calculators and ＀nds 4 defective calculators. Estimate the total number of defective calculators out of the 15,000.

Answer 1

To estimate the total number of defective calculators out of the 15,000 based on the sample, you can use the concept of proportion.

First, calculate the proportion of defective calculators in the sample:
Proportion of defective calculators in sample = (Number of defective calculators in sample) / (Total sample size)
Proportion = 4 / 450 ≈ 0.0088889

Now, use this proportion to estimate the total number of defective calculators out of the 15,000:
Estimated defective calculators = Proportion × Total population size
Estimated defective calculators = 0.0088889 × 15,000 ≈ 133.3335

Based on this estimation, there are approximately 133.33 defective calculators out of the 15,000 produced by the manufacturer. Since you can't have a fraction of a calculator, you would round this to the nearest whole number, so the estimated total number of defective calculators would be around 133.