I have the information about processing timing of db transactions.
I was wondering if the info I have is sufficient to plot a normal probability distribution graph.
Data available:
560000 hits
Average processing time: 171 ms
Minimum processing time: 2 ms
Maximum processing time: 9909 ms
Standard deviation: 357 ms
Can I plot the graph according to this information or I need additional info?
A normal distribution does not actually have any minimum and maximum. So you ignore these two parameters. But yes, a normal distribution is determined by its mean and standard deviation, and the formula is given by: $$ f(x) = \frac{1}{\sigma \sqrt{2\pi}} e^{-(x - \mu)^2 / 2\sigma^2}, $$ where $\mu$ is mean and $\sigma$ is standard deviation. So just plug in \begin{align*} \mu &= 171 \text{ ms} \\ \sigma &= 357 \text{ ms}. \end{align*}
HOWEVER: Note that this normal distribution you get is far from being close to the data you provide! In fact, under this distribution, there is a 31.597% chance of getting a negative number. In contrast, your data has no negative numbers. So you might want to seriously consider modeling your data with something other than a normal distribution, before just jumping to the conclusion that the data is approximately normal. Bjorn Friedrich in the comments suggests that a Log-normal distribution may be more appropriate.