CK-12 Probability and Statistics - Advanced

http://www.ck12.org Chapter 5. Normal Distribution

In one of the few instances in beginning statistics that we use algebra, plug in the known quantities into thez−score
formula:

z=

x−μ

σ

− 1. 645 ≈

20 −μ

4. 5

− 1. 645 ∗ 4. 5 ≈ 20 −μ

− 7. 402 − 20 ≈−μ

− 27. 402 ≈−μ

μ≈ 27. 402

Example:

For a normally distributed random variable,μ= 83 ,x=94, andp=.90, findσ.

Solution:

Again, let’s first look at a sketch of the distribution.

Since about 97.5% of the data is below 2 standard deviations, it seems reasonable to estimate that thex−value is
less than two standard deviations away andσmight be around 7 or 8.

Again, use invNorm to calculate thez−score. Remember that we are not entering a mean or standard deviation, so
the result is fromμ=0 andσ=1.