Using the standard normal curve find the zscore if the area

Using the standard normal curve find the z-score if the area

a)    between –z and z is 99.49

b)    to the right of z is 34.46.

Solution

a)

In this case, then by symmetry, the area to the left of -z is (1-0.9949)/2 = 0.00255.

Thus, by table/technology, the value of -z with this left tailed area is

-z = -2.80064873

Hence,

z = 2.80064873 [ANSWER]

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b)

If the area to the right of z is 0.3446, then the left tailed area is 0.6554.

We get the z score from the given left tailed area. As      
      
Left tailed area =    0.6554  
      
Then, using table or technology,      
      
z =    0.399940964   [ANSWER]