# How to find sample variance given population mean and variance (no specific data)

#### IngotAct

##### New Member
Hi, I am working on the following problem:

Population Mean = 1000
Population Std. Dev. = 400

Sample N=25
How many, from the sample of 25, are greater than 1000 if the sample mean is 1100.

Can I assume the sample std. dev. is the same as the population?

Does anyone know how I would go about solving this?

#### Dason

Is that the full question or did it ask for the expected number that are greater than 1000?

#### IngotAct

##### New Member
Right, it asked for the expected number that are greater than 1000

#### BGM

##### TS Contributor
Do you have more information? E.g. any distributional assumption? It may be better for you to type the whole question/whole piece of information you have.

Anyway it seems to ask for the following quantity:

$$E\left[\sum_{i=1}^N \mathbf{1}\{X_i > \mu\}\Bigg|\bar{X} = x\right] = \sum_{i=1}^N \Pr\{X_i > \mu|\bar{X} = x\}$$

With the limited information given, it seems that at most you can obtain a bound for this like the Chebyshev Inequality.