MHB How to Solve for a Given Probability in a Standard Normal Distribution Table?

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To solve for a given probability in a standard normal distribution table, one must understand the relationship between the cumulative distribution functions. For the probability P(0<z<a) = 0.3554, it requires an inverse table look-up. This involves determining the area from negative infinity to a, which can be calculated as P(-∞<z<a) - P(-∞<z<0). By finding the corresponding value in the standard normal distribution table, the solution can be derived. The process is illustrated with an attachment for clarity.
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Question by KS, reposted from Yahoo Questions

P(0<z<a) = 0.3554 solution
help!
i have to find a

Since z is used for the variable we may assume that this is a normal distribution question, and that Z is a RV with a standard normal distribution.

In which case we have a problem asking us to do an inverse table look-up in a table of standard normal distribution. These come in two varieties one gives exactly the probability you require the area under the curve from 0 to a, the other gives the area from -infinity to a. In the latter case for you need:

##P(0<z<a)=P(-\infty<z<a) - P(-\infty< z<0) = P(-\infty< z< a) - 1/2##.

So for this type of table we look up:

##P(-\infty< z< a)=0.8554##

The way an inverse table look up is done is to look in the body of the table for the value of the probability and the value of a is then the corresponding value you would have looked up. This is shown in the attachment:

View attachment 85

CB
 

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  • InverseTable.PNG
    InverseTable.PNG
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