Normal distribution, Exercises of Biostatistics

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Normal Distribution

Lt.Col.Dr Osama Atoom Lecture 5

iostatistics

Objectives

 Learning Objective

• To understand the topic on Normal Distribution and

its importance in different disciplines.

 Performance Objectives

At the end of this lecture the student will be able to:

 Draw normal distribution curves and calculate the

standard score (z score)

 Apply the basic knowledge of normal distribution to

solve problems.

 Interpret the results of the problems.

Carl Gauss 

The normal curve is often called the

Gaussian distribution, after Carl Friedrich

Gauss, who discovered many of its

properties. Gauss, commonly viewed as

one of the greatest mathematicians of all

time (if not the greatest), is honored by

Germany on their 10 Deutschmark bill.

What is Normal Distribution?

 It is defined as a continuous frequency

distribution of infinite range* (can take any

values not just integers as in the case of

binomial).

 This is the most important probability

distribution in statistics and important tool in

analysis of epidemiological data and

management science.

The normal distribution  (^) symmetric,  (^) bell-shaped

Probability

X

Characteristics of Normal Distribution

 Hence Mean = Median = Mode

 The total area under the curve is 1 (or 100%)

 Normal Distribution has the same shape as

Standard Normal Distribution.

In a Standard Normal Distribution:

The mean (μ ) = 0 and

Standard deviation (σ) =1) =

Some examples of things that follow a Normal Distribution

Heights of people

Size of things produced by machines

Errors in measurements  (^) Blood Pressure  (^) Test Scores

Irwin/McGraw-Hill © The McGraw-Hill Companies,

• 5

1. 4
2. 3
3. 2
4. 1 . 0 x f^ (^ x r a l i t r b u i o n : m = 0 , s^2 = 1 Characteristics of a Normal Distribution

Mean, median, and

mode are equal

Normal

curve is

symmetrical

Theoretically,

curve

extends to

infinity

a

Effects of m and s (^140 160 180160 180 ) shifts the curve along the axis (^200 ) 2 =^174 1 = 2 =^6 1 =^6 2 =^12 1 =^2 =^170 increases the spread and flattens the curve

(a) Changing (b) Increasing

1 =^160

The Normal Distribution

X

Changing μ shifts the

distribution left or

right.

Changing σ

increases or

decreases the

spread.

Why do we need to know Standard Deviation?

Any value is

likely to be within 1 standard deviation of the mean

very likely to be within 2 standard deviations

almost certainly within 3 standard deviations

Comparing X and Z units Z 100 0 2. 200 X (m^ = 100,^ s^ = 50)

(m = 0, s = 1)

Z Score

Z = X - μ

Z indicates how many standard deviations away from the mean the point x lies.  (^) Z score is calculated to 2 decimal places. σ