Solve the problem.
-According to a college survey, 22% of all students work full time. Find the standard deviation for the number of students who work full time in samples of size 16.
A)3.52
B)2.75
C)1.88
D)1.66

Question

Quizplus · Accepted Answer

The standard deviation for the number of students who work full time in samples of size $n$ can be found using the formula for the standard deviation of a proportion in a sample: $\sigma_{\hat{p}} = \sqrt{\frac{p(1-p)}{n}}$, where $p$ is the proportion of students who work full time (0.22) and $n$ is the sample size (16). Plugging in the values, we get $\sigma_{\hat{p}} = \sqrt{\frac{0.22(1-0.22)}{16}} = \sqrt{\frac{0.22(0.78)}{16}} = \sqrt{\frac{0.1716}{16}} = \sqrt{0.010725} = 0.10357$. This is the standard deviation of the proportion, but to find the standard deviation of the number of students, we multiply by the sample size: $0.10357 \times 16 = 1.65712$, which rounds to 1.66.

Solve the Problem. -According to a College Survey, 22% of All Students Work