Given that Z is a standard normal random variable what is th

Given that Z is a standard normal random variable, what is the value of Z if the area to the left of Z is 0.0559?

Simmilarly, what is the value of Z if the area to the right of Z is 0.1112?

Are these values (.0559 and .1112) probabilities??

Solution

Given that Z is a standard normal random variable, what is the value of Z if the area to the left of Z is 0.0559?

We get the z score from the given left tailed area. As          
          
Left tailed area =    0.0559      
          
Then, using table or technology,          
          
z =    -1.590154428   [ANSWER]

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Simmilarly, what is the value of Z if the area to the right of Z is 0.1112?

We get the z score from the given left tailed area. As          
          
Left tailed area = 1 - 0.1112 = 0.8888      
          
Then, using table or technology,          
          
z =    1.220171153   [ANSWER]

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Are these values (.0559 and .1112) probabilities?? [YES, they are areas under the standard normal curve]