AP Statistics: Section 2.2 B
Recall finding a z-score in section 2.1:
X 
z = ------------.

We can use this formula to take
any particular observation in a
Normal distribution and convert it
to a z-score. This new distribution
of z-scores is called the
standard Normal distribution
____________________________.
Its mean will be _____
0 and its
standard deviation will be _____.
1
The notation for the standard
Normal distribution is ______.
N (0,1)
The standard Normal distribution is
a density curve and thus the area
under the curve must equal ____
1
Any question about the proportion
of observations in a particular
interval can be answered by finding
the area under the curve.
Turn to Table A in the front of your
text.
Note that table A always gives the
area to the left of
the z-score.
1  .9066  .0934
Calculator:
2nd VARS (DISTR)
2:normalcdf(
ENTER
normalcdf(lower limit, upper limit)
normalcdf(1.32, 10000)
.0934
.8413  .2843  .5570
normalcdf(-.57, 1)
.5570
Normal Distribution Calculations
We can answer any question about
proportions of observations in a
Normal distribution by
____________
standardizing and then using the
Standard Normal table.
240  170
z
 2.33
30
1  .9901  .0099
Calculator:
normalcdf(240,10000,  ,  )
normalcdf(240, 10000, 170, 30)
.0098
150  170
z
 .67
30
190  170
z
 .67
30
.7486  .2514  .4972
Calculator:
normalcdf(150,190,170,30)
.4950
x  170
 .67 
30
 .67
x  149.9
Calculator:
2nd VARS (DISTR)
3: invNorm(
ENTER
invNorm(area to left,  , )
invNorm(.25, 170, 30)
x  149.765
x  170
.84 
30
x  195.2
.84
invNorm(.8, 170, 30)
x  195.249