Area Under Normal Curve

Example

Considering our example above where μ = 2, σ = 1/3, then

One-half standard deviation = σ/2 = 1/6, and

Two standard deviations = 2σ = 2/3

So 1/2 s.d. to 2 s.d. to the right of μ = 2 will be represented by the area from x1= 2 1/6 to x2= 2 2/3  . This area is graphed as follows:

The area above is exactly the same as the area

z1 = 0.5 to z2 = 2

in the standard normal curve:


μ = 0, σ = 1

Example

Find the area under the standard normal curve for the following, using the z-table. Sketch each one.

(a) between z = 0 and z = 0.78

(b) between z = -0.56 and z = 0

(c) between z = -0.43 and z = 0.78

(d) between z = 0.44 and z = 1.50

(e) to the right of z = -1.33.

Answer

From the z-table:

(a) 0.2823

 

 

(b) 0.2123

(c) 0.1664 + 0.2823 = 0.4487

(d) 0.4332 – 0.1700 = 0.2632

(e) 0.4082 + 0.5 = 0.9082

normalZ- tablearea
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