Can I assume this data will be normally distributed? If I were to get a sample of random people to solve a Sudoku puzzle, recording the time is takes them to complete it, can I model the range of times as a normal distribution with a mean $\mu$ and variance $\sigma^2$?

If it can't be modelled this way, how else could I do it?
@Ben Harris: drhab is right. The normal distribution is unlimited along the $x$-Axis, whereas your time data are limited by $0$ on the left. How about a Poisson Distribution(url=https://en.wikipedia.org/wiki/Poisson_distribution)? This is reasonable, since if I start my puzzle at time $0$, and I am done at time $t\geq0$, then I am also done at every $t+\epsilon$ for any $\epsilon\geq 0$.
@Ben Harris: drhab is right. The normal distribution is unlimited along the $x$-Axis, whereas your time data are limited by $0$ on the left. How about a Poisson Distribution(url=https://en.wikipedia.org/wiki/Poisson_distribution)? This is reasonable, since if I start my puzzle at time $0$, and I am done at time $t\geq0$, then I am also done at every $t+\epsilon$ for any $\epsilon\geq 0$.