# How do I find the Z score for a statistic without standard deviation given Pop mean=.05%, n=100, Sample mean of .11%?

Jun 6, 2015

By definition, Z score is:
$z = \frac{x - \mu}{\sigma}$
where $x$ is your datum, $\mu$ is the mean of your population and $\sigma$ is its standard deviation. Basically, it's a measure of deviation from the mean in units of standard deviation.

Unless I misunderstood your problem, I see no way you can calculate this number without knowing a standard deviation.

Dec 7, 2016

I think the problem is really about a proportion so you do not need the standard deviation to find the standardized test statistic z. See the Explanation for the formula.

#### Explanation:

In your question, the sample proportion (p-hat) is 0.11%. The population proportion, p, is 0.05%. Use the following procedure: