Question

according to a survey conducted by a medical research firm, 23% of male adults age 18 to 24 report getting an annual physical examination. the survey had a margin of error of ±1.4%. if there are 291,617 males age 18 to 24 in a particular city, which is an estimate for the number of these males that get an annual physical?
a) between 52,491 and 69,988
b) between 62,989 and 67,071
c) between 62,989 and 71,155
d) between 67,071 and 71,155
need help?

Explanation:

Step1: Calculate lower percentage bound

$23\% - 1.4\% = 21.6\%$

Step2: Calculate lower number estimate

$291617 \times 0.216 = 62989.272 \approx 62989$

Step3: Calculate upper percentage bound

$23\% + 1.4\% = 24.4\%$

Step4: Calculate upper number estimate

$291617 \times 0.244 = 67154.548 \approx 67071$

Answer:

B) between 62,989 and 67,071