z = (x-mu)/sigma where x is the individual score, mu is the average score and sigma is the standard
deviation. Normal distribution gives the z score, while x is the score for an individual. If both x and
mu are missing, you would have two unknowns, which require two equations to solve.
Inverse Normal can be used to find a z-score, given sufficient information.
If X is a random variable with a distribution of N(μ, σ), find:
p(µ−3σ ≤ X ≤ µ+3σ)

Approximately
99.74%
of the X values are less than three standard deviations from the
mean.

The usual statement for a standard score is
and you can solve for any one of the four given the other three with
If
you also have a probability such as
and a normal distribution then you can use the standard normal cumulative
distribution function and its inverse to say
So, knowing
p
or
z
implies you know the other.
You can then extend this for example to
or similar results.
In many problems, not knowing two of
x
or
μ
or
σ
or both of
z
and
p
could
cause difficulties in being able to determine them.
Probability percentages may be easier to handle rewritten as decimal fractions:
for example,
95
%
=
0.95
95%=0.95
.

In step 1, we need to set up our statistical hypothesis.
We will now use the statistical notation of H‐zero or H‐naught to represent the null hypothesis
and H‐a to represent the alternative hypothesis.
The null hypothesis suggests nothing special is going on; in other words, there is no change from
the status quo, no difference from the traditional state of affairs, or no relationship – depending
on the situation at hand.
In contrast, the alternative hypothesis disagrees with this, stating that something is going on, or
there is a change from the status quo, or there is a difference from the traditional state of affairs.
The alternative hypothesis, Ha, usually represents what we want to check or what we suspect is
really going on.
In Step 2: We Collect data, check conditions, and Summarize Data
We look at sampled data in order to draw conclusions about the entire population.
In the case of hypothesis testing, based on the data, you draw conclusions about whether or not
there is enough evidence to reject Ho.
There is, however, one detail that we would like to add here. In this step we collect data and
summarize it.
In Step 3 We Assess the Evidence
This is the step where we calculate how likely is it to get data like that observed (or more
extreme) ASSUMING Ho is true.