Section 6.2

Reading a Normal Curve Table

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Copyright © 2008 by Hawkes Learning

Systems/Quant Systems, Inc.

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The probability of a random variable having a value in a given range is equal to the area under the curve in that region.

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Probability of a Normal Curve:

Continuous Random Variables

6.2 Reading a Normal Curve Table

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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

Continuous Random Variables

6.2 Reading a Normal Curve Table

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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.

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Area to the Left of z:

Continuous Random Variables

6.2 Reading a Normal Curve Table

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:

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Continuous Random Variables

6.2 Reading a Normal Curve Table

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TI-84 Plus Instructions:

1. Press 2nd, 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

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Area to the Right of z:

Continuous Random Variables

6.2 Reading a Normal Curve Table

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:

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Continuous Random Variables

6.2 Reading a Normal Curve Table

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TI-84 Plus Instructions:

1. Press 2nd, 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

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Area Between z1 and z2:

Continuous Random Variables

6.2 Reading a Normal Curve Table

a. z1 = 1.16, z2 = 2.31

0.1126

b. z1 = 2.76, z2 = 0.31

0.6188

c. z1 = 3.01, z2 = 1.33

0.0905

Find the area between z1 and z2 :

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Continuous Random Variables

6.2 Reading a Normal Curve Table

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TI-84 Plus Instructions:

1. Press 2nd, then VARS

2. Choose 2: normalcdf(

3. The format for entering the statistics is normalcdf(1E99,z2)

4. Select

5. 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).

Continuous Random Variables

6.2 Reading a Normal Curve Table

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Area in the Tails:

Continuous Random Variables

6.2 Reading a Normal Curve Table

a. z1 = 1.25, z2 = 2.31

0.9048

b. z1 = 1.45, z2 = 2.40

0.6188

c. z1 = 1.05, z2 = 1.05

0.0905

Find the area in the tails:

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Continuous Random Variables

6.2 Reading a Normal Curve Table

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TI-84 Plus Instructions:

1. Press 2nd, then VARS

2. Choose 2: normalcdf(

3. The format for entering the statistics is normalcdf(1E99,z1)

4. Select

5. 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).

Continuous Random Variables

6.2 Reading a Normal Curve Table

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Finding Area:

Continuous Random Variables

6.2 Reading a Normal Curve Table