6.4 Standard Normal
Distribution
Objectives:
By the end of this section, I will be
able to…
1)
Find areas under the standard normal
curve, given a Z-value.
2)
Find the standard normal Z-value, given an
area.
The Standard Normal Curve
 It
is a normal distribution with
a
mean of 0 and
a
standard deviation of 1
 AREA
= PROBABILITY
Standard Normal Curve
Three Cases for Finding Areas
 Finding
areas to the LEFT of z.
 Finding areas to the RIGHT of z.
 Finding areas between two z values.
Case 1
1.
Find the area to the left of z = 1.34
Step 1: Draw a normal curve
Step 2: Mark the mean ( = 0)
Step 3: Mark the z value(s)
Step 4: Shade the area
0.9099
Step 5: Use the z table to find the area
0
1.34
Case 2
1.
Find the area to the right of
z = -2.06.
A = 1 - 0.0197
A = 0.0197
-2.06
A = 0.9803
0
Case 3
2. Find the area between z = -1.06 and
z = 2.38 in a standard normal curve.
A = 0.9913 – 0.1446
A = 0.8467
A = 0.9913
A = 0.1446
-1.06
0
2.38
Working Backwards
2. Now you are GIVEN the AREA and
Go to the chart and
must find the z-score.
find the closest
value to 0.87
z = 1.12 has an area of 0.8686
z = 1.13 has an area of 0.8708
Which is closer?
A = 0.87
0
z = 1.13
z1
z = 1.13
Working Backwards
Find the standard normal z-value that has
an area of 0.24 to the RIGHT of it.
1 – 0.24
A = 0.76
Go to Chart
Find the area of the ? in order to
find the missing z value.
z = 0.70 is A = 0.7580
z = 0.71 is A = 0.7611
A =? 0.76
A = 0.24
0
z1
z = 0.71
PRACTICE

Page 293- 294

#6, 10, 16, 22, 28,
ON A SEPARATE SHEET OF PAPER
WITH A PARTNER.
 IT WILL BE GRADED. YOU MUST
DRAW DIAGRAMS.
