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Example For the z-score, find the probability that z lies between (i) 0 and 1.98 (ii) -0.68 and 0 (iii) 1.35 to 2.18 ( iv) -2.18 to - 1.35 (v) To the left of -0.6 (vi) To the right of z = -1.28 (vii) -2.18 to 1.35

Solution :     Here we are given z-scores, we have only to
                     refer to the table and find the areas
                     corresponding to these numbers and add or
                     subtract accordingly as the numbers are negative
                     or positive.

i)   From the table z = 1.98 gives z = 1.98 is 0.4762

   Thus P ( 0 £ z £ 1.98 ) = 0.4762 i.e. 47% of area.

Note : For z = 1.18 looking into the table of z-score, first find 4.9 in the first column and move to your right along the same horizontal row till you get column with head 0.08. The intersection of the two is 0.4762 (refer to Table 1)

See this ® First column 0.01      0.02     .............0.08      0.09

z)

     1.9     0.4713    0.4719 ............    0.4767



  1. Area from z = -0.68 to 0 is the same as from 0 to 0.68 by symmetry. hence for z = 0.68 it is 0.2518.

           \ P ( -0.68 £ z £ 0 = 0.2518 i.e. 25% of area.

iii) Area from 0 to 1.35 is 0.4115 and from 0 to 2.18 is 0.4854. The required area is the difference between the two areas.

     \ P ( 1.35 £ z £ 2.18 = 0.4854
- 0.4115

         = 0.739

     i.e. 7% of area.

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Index

7. 1 Introduction
7. 2 Trial
7. 3 Sample Space
7. 4 Definition of Probability
7. 5 The Laws of Probability
7. 6 Conditional Probability
7. 7 Theoretical Distribution
7. 8 Binomial Distribution
7. 9 Normal Distribution

Chapter 8





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