Question

from 15,000 graphing calculators produced by a manufacturer, an inspector selects a random sample of 525 calculators and finds 6 defective calculators. estimate the total number of defective calculators out of the 15,000.
there are about \\(\square\\) defective calculators out of the 15,000.
(round to the nearest whole number as needed.)

Explanation:

Step1: Find the proportion of defective calculators in the sample

The sample size is 525, and the number of defective calculators in the sample is 6. So the proportion of defective calculators in the sample is $\frac{6}{525}$.

Step2: Estimate the number of defective calculators in the total production

The total number of calculators produced is 15,000. We multiply the total number by the proportion of defective calculators in the sample: $15000\times\frac{6}{525}$.
First, simplify $\frac{6}{525}=\frac{2}{175}$. Then $15000\times\frac{2}{175}=\frac{30000}{175}\approx171.43$. Rounding to the nearest whole number, we get 171.

Answer:

171