Next: Exponential Distribution
Previous: Transformation to the Standard Normal Distribution

Approximating Discrete Distributions: Sometimes even though a r.v. is discrete and takes on values from some countable set, we can approximate this with a (continuous) Normal distribution. This is most useful when the number of values possible is relatively large and the probability histogram for the discrete r.v. has a "bell-shaped" structure to it. This has to be done carefully...

Recall that each rectangle in the probability histogram represents a single value around which we "center" the rectangle. This necessitates a so-called continuity correction when we look up standard Normal tables. For example, assuming an x-axis scale of 1 unit for each rectangle (its width)

• to find P(X£ 23), we look up F[(23.5-m)/s]; not F[(23-m)/s]
• to find P(X³ 23), we look up 1- F[(22.5-m)/s]; not 1- F[(23-m)/s ]
• to find P(X=23), we look up F[(23.5-m)/s] - F[(22.5-m)/s ]

Approximating the Binomial Distribution: If X is a binomial r.v. with parameters n and p, we may approximate it with a Normal r.v. with mean m =np and variance s²=np(1-p), so that

Next: Exponential Distribution
Previous: Transformation to the Standard Normal Distribution