Is it possible to estimate the standard deviation of a normal distribution if I only have the mean of the population? I'm not a math or statistics expert and only have a self-taught basic understanding of these things. I'm working on a problem where I know the mean of the population and I want to estimate the standard deviation. This assumes a normal distribution of the population. Is this possible?
For example, if the mean if 32, with possible values between 0 and 100, can I calculate what the standard deviation is with just this information?
Thank you for your help!
 A: Normal distributions with very different standard deviation can have the same mean, so knowing the mean doesn't tell you which standard deviation you had. Indeed for samples from the normal distribution, the sample mean and sample standard deviation are independent, so the mean doesn't tell you anything about the standard deviation.

if the mean if 32, with possible values between 0 and 100

Then you cannot have a normal distribution (normal distributions are necessarily unbounded). On the other hand, the mean and the two bounds together do impose an upper limit on the standard deviation, but it's pretty weak.
A: The later clarification, in a comment to the question, that these are "win rates" ranging from 0% to 100% makes this a bit more feasible than the earlier answer from @Glen_b posted before that information was available.
You might think of this problem like flipping a biased coin, with a probability p of showing "heads" (a "win"; p = 0.32 for your example). Flipping this coin N times (e.g., N sales attempts) is a binomial sampling problem in terms of the number of "wins." This can look like a normal distribution, but as values can only be non-negative integers it can't strictly be normal.
As documented on the linked Wikipedia page and on this Cross Validated page, the variance of the estimate of p among repeated trials with N flips per trial is: $p(1-p)/N$. So to determine whether a particular sales rep is a "model" or "needs help," you also have to take into account the number of sales attempts.
