# What is the z-score of sample X, if n = 256, mu= 67, St. Dev. =80, and mu_X =56?

Apr 22, 2016

It is -2.2. That means that you are between 95-97% of the curve probability density function.

#### Explanation:

It is -2.2000. That means that you are between 95-97% of the curve probability density function.

It is calculated using, assuming you random variable is normal, otherwise you should use the t-student, which is similar, but with a "fatter" tale:

$z = \frac{{\mu}_{X} - \mu}{\frac{\sigma}{\sqrt{n}}}$, which is a normal distribution with mean 0 and standard deviation 1. I have used $\sigma =$standard deviation

This formula is value for N samples from a normally distributed random variable, with known stDev and meam, which was given in the question heading.