1. Reading a Normal Curve Table
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HAWKES LEARNING SYSTEMS
math courseware specialists
Section 6.2
Reading a Normal Curve Table

2. HAWKES LEARNING SYSTEMS
math courseware specialists
Continuous Random Variables
6.2 Reading a Normal Curve Table
Probability of a Normal Curve:
The probability of a random variable (X) having a value (e.g. 80) in a given range (e.g. 50 to 100) is equal to the area under the curve in that region.

3. HAWKES LEARNING SYSTEMS
math courseware specialists
Continuous Random Variables
6.2 Reading a Normal Curve Table
Standard Normal Distribution Table:
Standard Normal Distribution Table from – to positive z z
0.00
0.01
0.02
0.03
0.04
0.0
0.5000
0.5040
0.5080
0.5120
0.5160
0.1
0.5398
0.5438
0.5478
0.5517
0.5557
0.2
0.5793
0.5832
0.5871
0.5910
0.5948
0.3
0.6179
0.6217
0.6255
0.6293
0.6331
0.4
0.6554
0.6591
0.6628
0.6664
0.6700
0.5
0.6915
0.6950
0.6985
0.7019
0.7054
0.6
0.7257
0.7291
0.7324
0.7357
0.7389
0.7
0.7580
0.7611
0.7642
0.7673
0.7704
0.8
0.7881
0.7910
0.7939
0.7967
0.7995

4. HAWKES LEARNING SYSTEMS
math courseware specialists
Continuous Random Variables
6.2 Reading a Normal Curve Table
Area to the Left of z:

5. z = 1.69 0.9545 z = -2.03 0.0212 z = 0 0.5000 z = 4.2 Approximately 1
HAWKES LEARNING SYSTEMS
math courseware specialists
Continuous Random Variables
6.2 Reading a Normal Curve Table
Find the area to the left of z:
z = 1.69
0.9545
z = -2.03
0.0212
z = 0
0.5000
z = 4.2
Approximately 1
z = - 4.2
Approximately 0

7. HAWKES LEARNING SYSTEMS
math courseware specialists
Continuous Random Variables
6.2 Reading a Normal Curve Table
Area to the Right of z:

8. HAWKES LEARNING SYSTEMS
math courseware specialists
Continuous Random Variables
6.2 Reading a Normal Curve Table
Find the area to the right of z:
z = 3.02
= 1 –
z = -1.70
= 1 –
z = 0
0.5000
z = 5.1
Approximately 0 = 1 –
z = - 5.1
Approximately 1 = 1 –

10. HAWKES LEARNING SYSTEMS
math courseware specialists
Continuous Random Variables
6.2 Reading a Normal Curve Table
Area Between z1 and z2:

11. HAWKES LEARNING SYSTEMS
math courseware specialists
Continuous Random Variables
6.2 Reading a Normal Curve Table
Find the area between z1 and z2 :
z1 = 1.16, z2 = 2.31
= Z2 – Z1 = – (YELLOW)
z1 = -2.76, z2 = 0.31
= Z2 – Z1 = – (GREEN)
z1 = -3.01, z2 = -1.33
= Z2 – Z1 = – (PINK)

13. HAWKES LEARNING SYSTEMS
math courseware specialists
Continuous Random Variables
6.2 Reading a Normal Curve Table
Area in the Tails:

14. HAWKES LEARNING SYSTEMS
math courseware specialists
Continuous Random Variables
6.2 Reading a Normal Curve Table
Find the area in the tails:
z1 = 1.25, z2 = 2.31
= Z1 + (1 – Z2) = (1 – ) - blue
z1 = -2.40, z2 = -1.45
= Z1 + (1 – Z2) = (1 – ) - red
z1 = -1.05, z2 = 1.05
= Z1 + (1 – Z2) = (1 – ) - green

20. Area = 1 – =

22. Area = (1 – ) =

24. Area = =