- Base of statistics

- Central limit theorem

- Testing of hypothesis

- Time series analysis

- Probability and distribution

- Normal distribution

- Design of experiment

- Correlation and regression analysis

- Statistical quality control

- Index number

- Vital statistics

**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

*z*_{1} = 0.5 to *z*_{2} = 2

in the standard normal curve:

**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.

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

,
,

Copyright 2012