Download Appendix 5.2 Normal Distribution Using MegaStat

Appendix 5.2
Normal Distribution Using MegaStat
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Appendix 5.2 ■ Normal Distribution Using MegaStat
Normal probability P(X ⬍ 31.2):
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Select Add-ins : MegaStat : Probability :
Continuous Probability Distributions
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In the “Continuous Probability Distributions”
dialog box, select the normal distribution tab.
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Enter the distribution mean (here equal to 33)
and the distribution standard deviation (here
equal to 0.7) in the appropriate boxes.
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Enter the value of x (here equal to 31.2) into
the “Calculate p given x” window.
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Click OK in the “Continuous Probability
Distributions” dialog box.
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The output includes P(lower), which is the area
under the specified normal curve below the given
value of x, and P(upper), which is the area under
the specified normal curve above the given value
of x. The value of z corresponding to the specified value of x is also included. In this case,
P(X ⬍ 31.2) equals P(lower) ⫽ .0051.
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(Optional) Click on the preview button to see the
values of P(lower) and P(upper) before obtaining
results in the Output worksheet.
Note that if a standard normal distribution is specified, 0 is entered in the mean box and 1 is entered in the standard deviation box—the “calculate P given X” box will read “Calculate P given z.” In this case, when we enter a
value of z in the “Calculate P given z” box, P(lower) and P(upper) are, respectively, the areas below and above the
specified value of z under the standard normal curve.
Normal probability P(X ⬍ 153 or X ⬎ 167). Enter 160.0833 into the Mean box and enter 5.3724 into the Standard
Deviation box. Find P(lower) corresponding to 153 and find P(upper) corresponding to 167. When these values are
placed in the output worksheet, use a simple Excel cell formula to add them together.
Inverse normal probability st such that P(X ⬎ st) ⫽ 0.05:
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Select Add-ins : MegaStat : Probability :
Continuous Probability Distributions
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Enter 100 into the Mean box and enter 10 into
the Standard deviation box.
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Select the “Calculate x given P” option.
Enter 0.05 into the P box. This is the area under
the normal curve we want to have above st (that is,
above the desired value of x).
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Click OK in the “Continuous Probability
Distributions” dialog box.
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The output includes P(lower) and P(upper)—as
defined above—as well as the desired value of x
(in this case x equals 116.45).