In a certain town,8% of female college students suffer from manic-depressive illness.If 230 of the female students are selected at random,what is the standard deviation of the number who suffer from manic-depressive illness?
A)4.11
B)4.29
C)211.6
D)18.4
E)16.93

Question

Quizplus · Accepted Answer

The standard deviation for a binomial distribution is given by the formula $\sqrt{n \cdot p \cdot (1-p)}$, where $n$ is the number of trials (in this case, 230 female students) and $p$ is the probability of success (in this case, 0.08 or 8% suffering from manic-depressive illness). Plugging in the values, we get $\sqrt{230 \cdot 0.08 \cdot (1-0.08)} = \sqrt{230 \cdot 0.08 \cdot 0.92} = \sqrt{16.896} \approx 4.11$.

In a Certain Town,8% of Female College Students Suffer from Manic-Depressive