Question

from 15,000 graphing calculators produced by a manufacturer, an inspector selects a random sample of 525 calculators and finds 5 defective calculators. estimate the total number of defective calculators out of the 15,000.
there are about \boxed{} 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 5. So the proportion \( p=\frac{5}{525} \).

Step2: Estimate the total number of defective calculators in 15,000.

We use the proportion to estimate the total. Let \( x \) be the total number of defective calculators. Then \( \frac{x}{15000}=\frac{5}{525} \). Solving for \( x \), we get \( x = 15000\times\frac{5}{525} \). Simplify \( \frac{5}{525}=\frac{1}{105} \), so \( x=\frac{15000}{105}\approx142.857 \). Rounding to the nearest whole number, we get 143.

Answer:

143