How To: Use the Normal Distribution Using the TI­89 1. Turn on the calculator by pressing the ON button (lowest left hand button). 2. Press APPS. 3. Then press ENTER twice. 4. You want to be on the screen where you can enter data into a list. 5. Press F5, this activates the choice from the top menu of F5­Distr. 6. To find the area under a normal curve with mean μ and standard distribution σ: Then select 4:Normal Cdf. a. For, P( a £ X £ b ), enter a in the box for Lower Value:, enter b in the box for Upper Value:, enter μ in the box for μ:, enter σ in the box for σ:. Then press ENTER. b. For P( X ³ a ), enter a in the box for Lower Value:, enter 10 ^ 99 in the box for Upper Value:, enter μ in the box for μ:, enter σ in the box for σ:. Then press ENTER. c. For P( X £ b ), enter “(­)” 10 ^ 99 in the box for Lower Value:, enter b in the box for Upper Value:, enter μ in the box for μ:, enter σ in the box for σ:. Then press ENTER. 7. To find the z­score with area p to the left: a. Select 2:Inverse. b. Then press the right arrow button. c. Then select 1:Inverse Normal… d. Press ENTER. e. In the box for Area: enter p. f. Press ENTER. 8. To find the x value with area p to the left when x ~ N(μ, σ): a. Select 2:Inverse. b. Then press the right arrow button. c. Then select 1:Inverse Normal… d. Press ENTER. e. In the box for Area: enter p. f. In the box for μ: enter μ. g. In the box for σ: enter σ. h. Press ENTER. Note: The “(­)” is indicating the button on the bottom row of the calculator, next to the “.”. Example to follow on next page ®
1 Example: 2. Press APPS. 3. Then press ENTER twice or until you see the screen where you input data into a list. 4. You want to be on the screen where you can enter data into a list. 5. Press F5, this activates the choice from the top menu of F5­Distr. 6. To find the area under a normal curve with mean 4 and standard distribution 2: Then select 4:Normal Cdf.
2 a. For, P( 1 £ X £ 2 ), enter 1 in the box for Lower Value:, enter 3 in the box for Upper Value:, enter 4 in the box for μ:, enter 2 in the box for σ:. Then press ENTER. b. For P( X ³ 1 ), enter 1 in the box for Lower Value:, enter 10 ^ 99 in the box for Upper Value:, enter 4 in the box for μ:, enter 2 in the box for σ:. Then press ENTER.
3 c. For P( X £ 1 ), enter “(­)” 10 ^ 99 in the box for Lower Value:, enter 1 in the box for Upper Value:, enter 4 in the box for μ:, enter 2 in the box for σ:. Then press ENTER. 7. To find the z­score with area 0.25 to the left: a. Select 2:Inverse. b. Then press the right arrow button. c. Then select 1:Inverse Normal…
4 d. Press ENTER. e. In the box for Area: enter 0.25. There should be a 0 in the box for μ: and a 1 in the box for σ:. f. Press ENTER (you may have to press ENTER twice). 8. To find the x value with area 0.25 to the left when x ~ N(4, 2): a. Select 2:Inverse. b. Then press the right arrow button.
5 c. Then select 1:Inverse Normal… d. Press ENTER. e. In the box for Area: enter 0.25. f. In the box for μ: enter 4. g. In the box for σ: enter 2.
6 h. Press ENTER (you may have to press ENTER twice).
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