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 having a value in a given range 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. The second decimal place is listed across the top row.
HAWKES LEARNING SYSTEMS
math courseware specialists
Continuous Random Variables
6.2 Reading a Normal Curve Table
Standard Normal Distribution Table (continued):
The standard normal tables reflect a z-value that is rounded to two decimal places.
The first decimal place of the z-value is listed down the left-hand column.
The second decimal place is listed across the top row.
Where the appropriate row and column intersect, we find the amount of area under the standard normal curve to the left of that particular z-value.
When calculating the area under the curve, round your answers to four decimal places.

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

6. 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. Press 2nd, then VARS (for the DISTR menu) Choose 2: normalcdf(
HAWKES LEARNING SYSTEMS
math courseware specialists
Continuous Random Variables
6.2 Reading a Normal Curve Table
TI-84 Plus Instructions:
Press 2nd, then VARS (for the DISTR menu)
Choose 2: normalcdf(
The format for entering the statistics is normalcdf(-1E99,z) (To get the E, press 2ND COMMA. The E means x 10power)
In the previous example, part a., we could have entered normalcdf(-1E99,1.69).

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

9. z = 3.02 0.0013 z = -1.70 0.9554 z = 0 0.5000 z = 5.1 Approximately 0
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
0.0013
z = -1.70
0.9554
z = 0
0.5000
z = 5.1
Approximately 0
z = - 5.1
Approximately 1

10. The format for entering the statistics is normalcdf(z,1E99)
HAWKES LEARNING SYSTEMS
math courseware specialists
Continuous Random Variables
6.2 Reading a Normal Curve Table
TI-84 Plus Instructions:
Press 2nd, then VARS
Choose 2: normalcdf(
The format for entering the statistics is normalcdf(z,1E99)
In the previous example, part a., we could have entered normalcdf(3.02,1E99).

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

12. 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
0.1126
z1 = -2.76, z2 = 0.31
0.6188
z1 = -3.01, z2 = -1.33
0.0905

13. The format for entering the statistics is normalcdf(-1E99,z2) Select -
HAWKES LEARNING SYSTEMS
math courseware specialists
Continuous Random Variables
6.2 Reading a Normal Curve Table
TI-84 Plus Instructions:
Press 2nd, then VARS
Choose 2: normalcdf(
The format for entering the statistics is normalcdf(-1E99,z2)
Select -
Repeat steps 1. through 3. this time entering the statistics as normalcdf(-1E99,z1)
In the previous example, part a., we could have entered normalcdf(-1E99,2.31) - normalcdf(-1E99,1.16).

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

15. 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
0.9048
z1 = -1.45, z2 = -2.40
0.6188
z1 = -1.05, z2 = 1.05
0.0905

16. The format for entering the statistics is normalcdf(-1E99,z1) Select +
HAWKES LEARNING SYSTEMS
math courseware specialists
Continuous Random Variables
6.2 Reading a Normal Curve Table
TI-84 Plus Instructions:
Press 2nd, then VARS
Choose 2: normalcdf(
The format for entering the statistics is normalcdf(-1E99,z1)
Select +
Repeat steps 1. through 3. this time entering the statistics as normalcdf(z2,1E99)
In the previous example, part a., we could have entered normalcdf(-1E99,1.25) + normalcdf(2.31,1E99).

17. HAWKES LEARNING SYSTEMS
math courseware specialists
Continuous Random Variables
6.2 Reading a Normal Curve Table
Finding Area: