My statistics professor gave us this question on our last exam and to solve for the standard deviation he just took the square root of the mean, is this correct?
Q: An average of 15 aircraft accidents occur each year (The World Almanac and Book of Facts, 2004). It is reasonable to believe that the accidents occur at random times and independently from one another. Given X represents the number of the accidents per year, answer the following questions:
1.The expected value of X: μ =?
2.The standard deviation of X: s =?
3.The probability of less than 10 accidents in one year: P(X < 10) =?
This looks like you are supposed to assume such accidents are a rare event. The question also states "accidents occur at random times and independently from one another.". These both hint that we should model the data using a Poisson distribution, $\operatorname{Po}(\lambda)$.
$\lambda$ is the mean, so $\lambda=15$. Of course, the Poisson distribution also has variance $\lambda$, and the s.d. is the square root of this.