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# sncr - 8325 7 7 Find P-1 35< z< 1 35 P-1 35< z< 1...

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Rules for the Standard Normal Curve October 6, 2005 1 . P (0 < z < k ) = Prob. at k from table 2 . P ( k 1 < z < k 2 ) = P (0 < z < k 2 ) - P (0 < z < k 1 ) 3 . P ( z > k ) = P ( z > 0) - P (0 < z < k ) , = 0 . 5 - P (0 < z < k ) 4 . P ( z < k ) = P (0 < z < k ) + P ( z < 0) , = P (0 < z < k ) + 0 . 5 5 . P ( - k < z < 0) = P (0 < z < k ) See Rule 1 6 . P ( - k 1 < z < k 2 ) = P ( - k 1 < z < 0) + P (0 < z < k 2 ) , = P (0 < z < k 1 ) + P (0 < z < k 2 ) 7 . P ( - k < z < k ) = P ( - k < z < 0) + P (0 < z < k ) , = P (0 < z < k ) + P (0 < z < k ) = 2 P (0 < z < k ) 8 . P ( z < - k ) = P ( z > k ) See Rule 3. 9 . P ( - k 1 < z < - k 2 ) = P ( k 2 < z < k 1 ) See Rule 2. 10 . P ( z > - k ) = P ( - k < z < 0) + P ( z > 0) , = P (0 < z < k ) + 0 . 5 1

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Examples to Accompany Rules 1. Find P (0 < z < 1 . 37). P (0 < z < 1 . 37) = 0 . 4147 2
2. Find P (1 . 28 < z < 2 . 46). P (1 . 28 < z < 2 . 46) = P (0 < z < 2 . 46) - P (0 < z < 1 . 28) , = 0 . 4931 - 0 . 3997 = 0 . 0934 . 3

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3. Find P ( z > 2 . 50). P ( z > 2 . 50) = P ( z > 0) - P (0 < z < 2 . 50) , = 0 . 5 - 0 . 4938 = 0 . 0062 . 4
4. Find P ( z < 0 . 83). P ( z < 0 . 83) = P (0 < z < 0 . 83) + P ( z < 0) , = 0 . 2967 + 0 . 5 = 0 . 7967 . 5

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5. Find P ( - 1 . 78 < z < 0). P ( - 1 . 78 < z < 0) = P (0 < z < 1 . 78) , = 0 . 4625 . 6
6. Find P ( - 2 . 21 < z < 1 . 02). P ( - 2 . 21 < z < 1 . 02) = P ( - 2 . 21 < z < 0) + P (0 < z < 1 . 02) , = P (0 < z < 2 . 21) + P (0 < z < 1 . 02) , = 0 . 4864 + 0 . 3461 = 0 . 8325 . 7

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7. Find

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Unformatted text preview: . 8325 . 7 7. Find P (-1 . 35 < z < 1 . 35). P (-1 . 35 < z < 1 . 35) = P (-1 . 35 < z < 0) + P (0 < z < 1 . 35) , = P (0 < z < 1 . 35) + P (0 < z < 1 . 35) = 2 P (0 < z < 1 . 35) , = 2(0 . 4115) = 0 . 8230 . 8 8. Find P ( z <-. 93). P ( z <-. 93) = P ( z > . 93) , = P ( z > 0)-P (0 < z < . 93) , = 0 . 5-. 3238 = 0 . 1762 . 9 9. Find P (-1 . 25 < z <-. 77). P (-1 . 25 < z <-. 77) = P (0 . 77 < z < 1 . 25) , = P (0 < z < 1 . 25)-P (0 < z < . 77) , = 0 . 3944-. 2794 = 0 . 1150 . 10 10. Find P ( z >-2 . 64). P ( z >-2 . 64) = P (-2 . 64 < z < 0) + P ( z > 0) , = P (0 < z < 2 . 64) + 0 . 5 , = 0 . 4959 + 0 . 5 = 0 . 9959 . 11...
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