Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Suppose one knew that 105 workers were evaluated by their boss. Such evaluation is distributed according to a normal distribution with mean $\mu$ and std. deviation $\sigma$. We also know that 20 workers received score less than 2, 25 were evaluated between 2 and 5, and 60 with evaluations bigger than 5. How can I form reasonable estimates for $\mu$ and $\sigma$?

share|cite|improve this question
up vote 1 down vote accepted

You know two proportions, i.e. two probabilities. So you know two areas under the normal curve for $N(\mu,\sigma)$.

There is a correspondence between $x$-values on the curve for $N(\mu,\sigma)$ and $z$-values on the curve for the standardized $N(0,1)$, for the same areas under the curves.

Hint: two equations and two unknowns.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.