Reading a Normal Curve Table Copyright © 2008 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. HAWKES LEARNING SYSTEMS math courseware specialists 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 0.7 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 Continuous Random Variables 6.2 Reading a Normal Curve Table 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 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

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

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 = 1 – 0.9987 z = -1.70 0.9554 = 1 – 0.0446 z = 0 0.5000 z = 5.1 Approximately 0 = 1 – 0.999999 z = - 5.1 Approximately 1 = 1 – 0.000001

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

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 = Z2 – Z1 = 0.9896 – 0.877 (YELLOW) z1 = -2.76, z2 = 0.31 0.6188 = Z2 – Z1 = 0.6217 – 0.0029 (GREEN) z1 = -3.01, z2 = -1.33 0.0905 = Z2 – Z1 = 0.0918 – 0.0013 (PINK)

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

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 – Z2) = 0.8944 + (1 – 0.9896) - blue z1 = -2.40, z2 = -1.45 0.9347 = Z1 + (1 – Z2) = 0.0082 + (1 – 0.0735) - red z1 = -1.05, z2 = 1.05 0.2937 = Z1 + (1 – Z2) = 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