HAWKES LEARNING SYSTEMS math courseware specialists Copyright 2008

HAWKES LEARNING SYSTEMS math courseware specialists Copyright © 2008 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 6. 2 Reading a Normal Curve Table

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.

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. 7580 0. 7611 0. 7642 0. 7673 0. 7704 0. 8 0. 7881 0. 7910 0. 7939 0. 7967 0. 7995

HAWKES LEARNING SYSTEMS math courseware specialists Area to the Left of z: Continuous Random Variables 6. 2 Reading a Normal Curve Table

HAWKES LEARNING SYSTEMS math courseware specialists Find the area to the left of z: 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 Continuous Random Variables 6. 2 Reading a Normal Curve Table

HAWKES LEARNING SYSTEMS math courseware specialists Area to the Right of z: Continuous Random Variables 6. 2 Reading a Normal Curve Table

HAWKES LEARNING SYSTEMS math courseware specialists Find the area to the right of z: a. z = 3. 02 0. 0013 = 1 – 0. 9987 b. z = -1. 70 0. 9554 = 1 – 0. 0446 c. z = 0 0. 5000 d. z = 5. 1 Approximately 0 = 1 – 0. 999999 e. z = - 5. 1 Approximately 1 = 1 – 0. 000001 Continuous Random Variables 6. 2 Reading a Normal Curve Table

HAWKES LEARNING SYSTEMS math courseware specialists Area Between z 1 and z 2: Continuous Random Variables 6. 2 Reading a Normal Curve Table

HAWKES LEARNING SYSTEMS math courseware specialists Continuous Random Variables 6. 2 Reading a Normal Curve Table Find the area between z 1 and z 2 : a. z 1 = 1. 16, z 2 = 2. 31 0. 1126 = Z 2 – Z 1 = 0. 9896 – 0. 877 (YELLOW) b. z 1 = -2. 76, z 2 = 0. 31 0. 6188 = Z 2 – Z 1 = 0. 6217 – 0. 0029 (GREEN) c. z 1 = -3. 01, z 2 = -1. 33 0. 0905 = Z 2 – Z 1 = 0. 0918 – 0. 0013 (PINK)

HAWKES LEARNING SYSTEMS math courseware specialists Area in the Tails: Continuous Random Variables 6. 2 Reading a Normal Curve Table

HAWKES LEARNING SYSTEMS math courseware specialists Continuous Random Variables 6. 2 Reading a Normal Curve Table Find the area in the tails: a. z 1 = 1. 25, z 2 = 2. 31 0. 9048 = Z 1 + (1 – Z 2) = 0. 8944 + (1 – 0. 9896) - blue b. z 1 = -2. 40, z 2 = -1. 45 0. 9347 = Z 1 + (1 – Z 2) = 0. 0082 + (1 – 0. 0735) - red c. z 1 = -1. 05, z 2 = 1. 05 0. 2937 = Z 1 + (1 – Z 2) = 0. 1469 + (1 – 0. 8531) - green

Area = 1 – 0. 0091 = 0. 9909

Area = 0. 0057 + (1 – 0. 5517) = 0. 4540

Area = 0. 6103 - 0. 0019 = 0. 6084