# Normal Probability Curve B.Ed (NPC Notes)

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## Normal Probability Curve

A normal Probability Curve (NPC) is a bell-shaped curve that shows a distribution of the probability of random variables. Normal Probability Curve (NPC) is also called the ‘Gaussian Curve Probability‘ in the name of a German mathematician.

In other words, a Normal Probability Curve is a bell-shaped curve that shows the probability distribution of a continuous random variable.

In short, the NPC represents a normal distribution. The total area under the NPC represents the sum of all probabilities of a random variable.

In statistics, NPC is very important because it is used to show the distribution of many naturally occurring variables, such as the weight of class 9th students, and the intelligence of class 10th students.

Like mathematics, the Normal Probability Curve is also important for social science s well as it can be used to represent past data in the form of a frequency distribution.

The Normal Curve is systematic about the mean/averages. The mean or average is the middle value and divides the area into two halves. The total area under the curve is equal to 1 and is determined by mean and standard deviation.

## Characteristics Of Normal Probability Curve

The following are the characteristics of the Normal Probability Curve (NPC):

1. The NPC curve is unimodal because it has only one mode.

2. All the central tendencies (Mean=Mode=Median) coincide in NPC.

3. The maximum ordinate occurs at the centre.

4. The normal curve is asymptotic to the x-axis.

5. The Normal Curve is symmetrical.

6. The height if NPC declines symmetrically.

7. The Normal Probability Curve is bilateral.

8. It is a mathematical modal in behavioral science.

9. It shows the greater percentage of cases at the middle of the distribution.

10. The scale of x-axis in normal curve is generalised by z-deviates.

11. The total area of NPC is divided into +ve and -ve Standard deviation.

12. The y-ordinate represents the height of the Normal Probability Curve.

13. The Mean of the Normal Curve is Meu (μ) and the Standard Deviation is represented by a random variable σ.

14. In NPC, the standard deviation is 50% larger than the Q.

## Applications of the NPC

Given are the few applications of NPC:

1. It is used to determine the limits of the scores which include a given percentage of cases.

2. To determine the percentage of cases that are above or below the given score or reference point.

3. To determine the percentage of the cases (in the normal distribution) within the given limits or scores.

### Conclusion

The Normal Probability Curve is widely used in understanding the distribution of factors in the population. All normal curves are bell shaped and show a clear image of the distribution.

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