Normal Probability Curve

Applications of Normal Probability Curve

A normal curve is a bell-shaped curve which shows the probability distribution of a continuous random variable. Moreover, the normal curve represents a normal distribution. The total area under the normal curve logically represents the sum of all probabilities for a random variable. Hence, the area under the normal curve is one. Also, the standard normal curve represents a normal curve with mean 0 and standard deviation 1. Thus, the parameters involved in a normal distribution is mean (μ) and standard deviation (σ).

Some of the most important applications of normal probability curve are as follows:

The principles of Normal Probability Curve are applied in the behavioral sciences in many different areas.

2.NPC is used to determine the percentage of cases in a normal distribution within given limits:

The Normal Probability Curve helps us to determine:

·         What percent of cases fall between two scores of a distribution?

·         What percent of scores lie above a particular score of a distribution?

·         What percent of scores lie below a particular score of a distribution?

v  NPC is used to determine the value of a score whose percentile rank is given:

By using NPC table we can determine the raw score of the individual if the percentile rank is given.

3. NPC is used to find the limits in a normal distribution which include a given percentage of cases:

When a distribution is normally distributed and what we know about the distribution is Mean and the Standard deviation at that time by using the table area under NPC we can determine the limits which include a given percentage of cases.

4. It is used to compare two distributions in terms of- overlapping:

If scores of two groups on a particular variable are normally distributed. What we know about the group is the mean and standard deviation of both the groups. And we want to know how much the first group over-laps the second group or vice-versa at that time we can determine this by using the table area under NPC.

5. NPC helps us in dividing a group into sub-groups according to certain ability and assigning the grades:

When we want to divide a large group in to certain sub-groups according to some specified ability at that time we use the standard deviation units of a NPC as units of scale.

6. NPC helps to determine the relative difficulty of test items or problems:

When it is known that what percentage of students successfully solved a problem we can determine the difficulty level of the item or problem by using table area under NPC.

7. NPC is useful to normalize a frequency distribution:

In order to normalize a frequency distribution we use Normal Probability Curve. For the process of standardizing a psychological test this process is very much necessary.

8. To test the significance of observations of experiments we use NPC:

In an experiment we test the relationship among variables whether these are due to chance fluctuations or errors of sampling procedure or it is real relationship. This is done with the help of table area under NPC.

9. NPC is used to generalize about population from the sample:

We compute standard error of mean, standard error of standard deviation and other statistics to generalize about the population from which the sample are drawn. For this computation we use the table area under NPC.