Normal Distribution

History• Its study dates back to the

eighteenth century when a mathematician Abraham De Moivre, developed the first developed the mathematical equation for the normal curve.

• And another mathematician, Carl Friedrich Gauss, developed the concept of the curve in the nineteenth century from a study of errors on repeated measurements of the same quantity. (Gaussian function, or informally the bell curve)

Definition • Normal distribution is a

probability distribution that plots all of its values in a symmetrical fashion and most of the results are situated around the probability's mean.

• It is graphically represented by a symmetrical bell- shaped curve that known as the

normal curve.

Properties of Normal Distribution

• The curve concentrated in the center and decreases on either side. This means that the data has less of a tendency to produce unusually extreme values, compared to some other distributions.

• The bell shaped curve is symmetric. This tells you that the probability of deviations from the mean is comparable in either direction.

The normal curve1. The mean, median, and

mode have the same value, and therefore are plotted on the same point along the horizontal axis.

2. The curve is symmetric above the vertical line which contains the mean.

3. The curve is asymptotic to the horizontal axis that is the curve extends indefinitely in both directions.

4. And lastly, the total area under the normal curve is equal to 1.

Standard Score (z- score)• The standard score

is the distance of the score from the mean in terms of the standard deviations the observed value lies above or below the mean of the distributions.

Application of the Normal curve

• Frequencies of scores in distributions can be found using the normal curve. Several problems on the different fields can be solved by applying the normal curve.

Example• There are two hundred

eighty incoming freshmen students at a certain College were given IQ test. Assuming that their IQs are normally distributed with a mean of 100 and a standard deviation of 15, find how many freshmen have an IQ of:

• 80 and lower

Computation using z-score

Find the z- score of 80

z = - 1.33 = 0.4082 (tabular)

Graph 0.50 – 0.4082 = 0.0918 or 9.18%

That’s all!Thank You!