stat1051_chpater1_lesson9(1)

stat1051_chpater1_lesson9(1) - Normal Distribution Normal...

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Normal Distribution Normal Distribution (Continued)

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2 Example 8.0 Find the real number a in each of the following cases. a) P(0 < Z < a) = 0.1915 b) P(Z < a) = 0.9821 c) P(-a < Z < a) = 0.6826 Remark: Note that we can use the normal tables to find the appropriate real numbers that gives these probabilities.
3 Solution: Example 8.0 Choose a real number a such that P(0 < Z < a) = 0.1915 Clearly from the table, P( Z < 0.5) = 0.6915. Hence P(0 < Z < 0.5) = 0.6915 – 0.5 = 0.1915. Therefore a = 0.5.

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4 Solution (cont) b) P(Z < a) = 0.9821 From the tables we see that a = 2.10 c) P(-a < Z < a) = 2 * P(0 < Z < a) = 0.6826 P(0 < Z < a) = 0.3413 which implies P(Z < a) = 0.8413 We see from the tables that a = 1
5 Steps for Finding Areas Steps for Finding areas Corresponding to a Normal Random Variable Sketch the distribution, locate mean, shade area of interest Convert to standard z values using Add z values to the sketch Use tables to calculate areas, making use of symmetry property where necessary σ μ - = x z

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This note was uploaded on 11/27/2011 for the course STAT 1051-10 taught by Professor Balaji during the Fall '11 term at GWU.

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stat1051_chpater1_lesson9(1) - Normal Distribution Normal...

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