Question

using a proportion
when jeremy surveyed thirty 7th-grade students at the community pool, he found that 2/15 had not read at least one book during july. he knows there are about 200 7th-grade students in his community, so he infers that about 40 of them did not read any books in july. is that a good inference? explain.

Explanation:

Step1: Find survey non-reader ratio

The fraction of non-readers in the sample is $\frac{2}{15}$.

Step2: Calculate expected non-readers

Multiply total students by the ratio: $200 \times \frac{2}{15} = \frac{400}{15} \approx 26.67$

Step3: Compare to Jeremy's inference

Jeremy's 40 non-readers is much higher than the expected ~27.

Answer:

No, this is not a good inference. Based on the survey proportion $\frac{2}{15}$, the expected number of 7th-grade students who did not read any books in July is approximately 27, not 40. Jeremy's inferred number does not match the proportion from his sample.