1. Section 6.2 Reading a Normal Curve Table HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved.

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

3. HAWKES LEARNING SYSTEMS math courseware specialists Standard Normal Distribution Table: Standard Normal Distribution Table from –  to positive z z0.000.010.020.030.04 0.00.50000.50400.50800.51200.5160 0.10.53980.54380.54780.55170.5557 0.20.57930.58320.58710.59100.5948 0.30.61790.62170.62550.62930.6331 0.40.65540.65910.66280.66640.6700 0.50.69150.69500.69850.70190.7054 0.60.72570.72910.73240.73570.7389 0.70.75800.76110.76420.76730.7704 0.80.78810.79100.79390.79670.7995 Continuous Random Variables 6.2 Reading a Normal Curve Table

4. HAWKES LEARNING SYSTEMS math courseware specialists Standard Normal Distribution Table (continued): Continuous Random Variables 6.2 Reading a Normal Curve Table 1.The standard normal tables reflect a z-value that is rounded to two decimal places. 2.The first decimal place of the z-value is listed down the left-hand column. 3.The second decimal place is listed across the top row. 4.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 Area to the Left of z: Continuous Random Variables 6.2 Reading a Normal Curve Table

6. a. z = 1.69 0.9545 b. z =  2.03 0.0212 c. z = 0 0.5000 d. z = 4.2 Approximately 1 e. z =  4.2 Approximately 0 Find the area to the left of z: HAWKES LEARNING SYSTEMS math courseware specialists Continuous Random Variables 6.2 Reading a Normal Curve Table

7. HAWKES LEARNING SYSTEMS math courseware specialists TI-84 Plus Instructions: 1.Press 2 nd, then VARS 2.Choose 2: normalcdf( 3.The format for entering the statistics is normalcdf(  1E99,z) In the previous example, part a., we could have entered normalcdf(  1E99,1.69). Continuous Random Variables 6.2 Reading a Normal Curve Table

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

9. a. z = 3.02 0.0013 b. z =  1.70 0.9554 c. z = 0 0.5000 d. z = 5.1 Approximately 0 e. z =  5.1 Approximately 1 Find the area to the right of z: HAWKES LEARNING SYSTEMS math courseware specialists Continuous Random Variables 6.2 Reading a Normal Curve Table

10. HAWKES LEARNING SYSTEMS math courseware specialists TI-84 Plus Instructions: 1.Press 2 nd, then VARS 2.Choose 2: normalcdf( 3.The format for entering the statistics is normalcdf(z,1E99) In the previous example, part a., we could have entered normalcdf(3.02,1E99). Continuous Random Variables 6.2 Reading a Normal Curve Table

11. HAWKES LEARNING SYSTEMS math courseware specialists Area Between z 1 and z 2 : Continuous Random Variables 6.2 Reading a Normal Curve Table

12. a. z 1 = 1.16, z 2 = 2.31 0.1126 b. z 1 =  2.76, z 2 = 0.31 0.6188 c. z 1 =  3.01, z 2 =  1.33 0.0905 Find the area between z 1 and z 2 : HAWKES LEARNING SYSTEMS math courseware specialists Continuous Random Variables 6.2 Reading a Normal Curve Table

13. HAWKES LEARNING SYSTEMS math courseware specialists TI-84 Plus Instructions: 1.Press 2 nd, then VARS 2.Choose 2: normalcdf( 3.The format for entering the statistics is normalcdf(  1E99,z 2 ) 4.Select  5.Repeat steps 1. through 3. this time entering the statistics as normalcdf(  1E99,z 1 ) In the previous example, part a., we could have entered normalcdf(  1E99,2.31)  normalcdf(  1E99,1.16). Continuous Random Variables 6.2 Reading a Normal Curve Table

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

15. a. z 1 = 1.25, z 2 = 2.31 0.9048 b. z 1 =  1.45, z 2 =  2.40 0.6188 c. z 1 =  1.05, z 2 = 1.05 0.0905 Find the area in the tails: HAWKES LEARNING SYSTEMS math courseware specialists Continuous Random Variables 6.2 Reading a Normal Curve Table

16. HAWKES LEARNING SYSTEMS math courseware specialists TI-84 Plus Instructions: 1.Press 2 nd, then VARS 2.Choose 2: normalcdf( 3.The format for entering the statistics is normalcdf(  1E99,z 1 ) 4.Select  5.Repeat steps 1. through 3. this time entering the statistics as normalcdf(z 2,1E99) In the previous example, part a., we could have entered normalcdf(  1E99,1.25)  normalcdf(2.31,1E99). Continuous Random Variables 6.2 Reading a Normal Curve Table

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