# Use the empirical rule to determine the approximate probability that a z value is between 0 and 1 on the standard normal curve.

Feb 20, 2015

You need to use a table of standar normal distribution curve. There are different kind of tables (cumulative, fi function, stc..), but your anwer is:
$P \left(0 < z < 1\right) = 0.34$

The empirical rule allows you to make a quick assessment of probability without using a table. Just memorise these three numbers:

0.34=34% is less than one standard deviation $\sigma$ higher than the mean $\mu$
$0.135 = 13.5$ is between $\sigma$ and $2 \sigma$ higher than $\mu$
0.025=2.5% is more than $2 \sigma$ higher than $\mu$

The same goes for values below $\mu$, as the normal curve is symmetrical. (So you have 68% of your values between $\mu - \sigma$ and $\mu + \sigma$, or between $z = - 1$ and $z = + 1$)

Remember every $\sigma$ translates to $1$ on the $z$-scale