Continuous Probability Distributions Study Guide (page 4)

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Updated on Oct 5, 2011

Example 8

Let X ~ N(10,5). Find P(X < 15).

Solution 8

P(X < 15)

= P(z < 1)

= 0.8413.

Notice that inside the parentheses, we had to transform both the X and the 15 to avoid changing the inequality. When working with X, we used symbols, and we used numbers when working with 15. However, we used the numbers that were associated with each symbol. Once we have the expression in terms of z, then the problem is equivalent to the earlier ones we worked. See Figure 11.15.

Figure 11.15

Example 9

Let X, N(5,2). Find X* such that P(X > X*) = 0.05.

Solution 9

Figure 11.16

First, we find z* such that P(z > z*) = 0.05. From our earlier work, we know that z* = 1.645. Then X* = μ 1 σz* = + 2(1.645) = 8.29.

Continuous Probabiity Distributions In Short

We have discussed two continuous distributions: the uniform and the normal. When every value in an interval is equally likely to occur, then we have a uniform distribution. The normal distribution is the most commonly used continuous distribution. Probabilities associated with a normal random variable must be found by using tables, calculators, or computers. When using tables, it is possible to use only one table. By tradition, the probabilities of a standard normal distribution are tabulated. Probabilities for other normal random variables are found by transforming the problem to one on the standard normal.

Find practice problems and solutions for these concepts a Continuous Probability Distributions Practice Questions.

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