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 having a value in a given range 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

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.

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

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).

HAWKES LEARNING SYSTEMS math courseware specialists Continuous Random Variables 6.2 Reading a Normal Curve Table 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 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

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).

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 z1 = -2.76, z2 = 0.31 0.6188 z1 = -3.01, z2 = -1.33 0.0905

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).

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 = -1.45, z2 = -2.40 0.6188 z1 = -1.05, z2 = 1.05 0.0905

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).

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