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Normal Probability Distribution for Beginning Statistics

By — McGraw-Hill Professional
Updated on Aug 12, 2011

Practice problems for these concepts can be found at:

Continuous Random Variables and Their Probability Distributions Solved Problems for Beginning Statistics

The most important and widely used of all continuous distributions is the normal probability distribution. Figure 6-5 shows the pdf for a normal distribution having mean μ and standard deviation σ.

Normal Probability Distribution

Table 6.1 gives some of the main properties of the normal curve shown in Fig. 6-5. Figure 6-6 shows two different normal curves with the same mean but different standard deviations. The larger the standard deviation, the more disperse are the values about the mean.

Normal Probability Distribution

Figure 6-7 shows two normal curves having equal standard deviations but different means. The normal curve with mean equal to 66 represents the distribution of adult female heights and the normal curve with mean equal to 70 represents the distribution of adult male heights.

Normal Probability Distribution

The equation of the pdf of a normal curve having mean μ and standard deviation σ is given in formula (6.5).

The two constants in the formula, e and π, are important constants in mathematics. The constant e is equal to 2.718281828 . . . and the constant π is equal to 3.141592654 . . . . The equation of the pdf for the normal curve is not used a great deal in practice and is given here for the sake of completeness.

Practice problems for these concepts can be found at:

Continuous Random Variables and Their Probability Distributions Solved Problems for Beginning Statistics

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