Theory of Normal Distribution and Standard Normal Distribution

Basic Definitions:

Central Limit Theorem: This theorem states that as the sample size rises, the sampling distribution of the sample means will become approximately generally distributed.

Correction for Continuity: It is a correction applied to transform a discrete distribution to a continuous distribution.

Finite Population Correction Factor: It is a correction applied to standard error of the means if the sample size is more than 5 percent of the population size and the sampling is completed with no replacement.

Sampling Distribution of the Sample Means: It is the distribution obtained by employing the means evaluated from random samples of a particular size.

Sampling Error: Difference that takes place between the sample statistic and population parameter due to the fact that the sample is not a perfect representation of population.

Standard Error or the Mean: It is the standard deviation of sampling distribution of sample means. It is equivalent to the standard deviation of the population divided by square root of the sample size.

Standard Normal Distribution: It is represented by the symbol z. It is basically a normal distribution in which the mean is 0 and the standard deviation is 1.

Z-score: It is also termed as z-value. In Z-score the mean is zero and the standard deviation is 1. The Z score is employed to represent the standard normal distribution.

Normal Distributions:

Any Normal Distribution:

1) Bell-shaped

2) Symmetric about mean

3) Continuous

4) Never touches the x-axis

5) Total area beneath curve is 1.00

6) Around 68% lies in 1 standard deviation of the mean, 95% in 2 standard deviations, and 99.7% in 3 standard deviations of the mean. This is the Empirical Rule.

7) Data values symbolized by x that has mean mu and the standard deviation sigma.

8) Probability Function is given by:

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Standard Normal Distribution:

1) Similar as the normal distribution, but also...

2) Mean is zero.

3) Variance is one.

4) Standard Deviation is one.

5) Data values symbolized by z.

6) Probability Function given by:

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