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# Applications of the Standard Normal Distribution

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Author: Bob Kibler

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Tutorial

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## "Do I get it" - Solutions

Mean = 28      Standard Deviation = 8      Data is normally distributed

1)  (26-28) / 8 = -0.25 (LOWER)

(34 - 28) / 8 = +0.75 (UPPER)

Using NORMALCDF --> 37.2%

2)   (26-28) / 8 = -0.25 (UPPER)

Since there is no LOWER we use -1E99 (negative infinity)

Using NORMALCDF --> 40.1%

3)  INVNORM(0.95) = +1.64       --> We use this since we want the farther right 5%, so 95% to the left

x = (1.64)(8) + 28 = 41.12 =  42 (Rounded)

4)  INVORM(0.4) = -0.25      INVNORM(0.6) = +0.25   --> Remember the symmetry

(Since the middle 20% is 10% on both sides of the mean, that leave 40% of the data below the LOWER

x = (-0.25)(8) + 28 = 26            x = (+0.25)(8) + 28 = 30