For a standard normal distribution with continuous random va

For a standard normal distribution with continuous random variable, Z.

b) Find Z_.096

c) Find 95th percentile.

Solution

a)

z1 = lower z score =    -2.6      
z2 = upper z score =     1.2      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.004661188      
P(z < z2) =    0.88493033      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.880269142   [ANSWER]

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b)

We get the z score from the given left tailed area. As          
          
Left tailed area =    0.096      
          
Then, using table or technology,          
          
z =    -1.304685385   [ANSWER]
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c)

We get the z score from the given left tailed area. As          
          
Left tailed area =    0.95      
          
Then, using table or technology,          
          
z =    1.644853627   [ANSWER]