A symmetric and bellshaped distribution has a mean of 70 and

A symmetric and bell-shaped distribution has a mean of 70 and a standard deviation of 10. Find the 16th and 95th percentile scores.

Solution

a)

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.16      
          
Then, using table or technology,          
          
z =    -0.994457883      
          
As x = u + z * s,          
          
where          
          
u = mean =    70      
z = the critical z score =    -0.994457883      
s = standard deviation =    10      
          
Then          
          
x = critical value =    60.05542117   [ANSWER, 16TH PERCENTILE]

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b)

First, 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      
          
As x = u + z * s,          
          
where          
          
u = mean =    70      
z = the critical z score =    1.644853627      
s = standard deviation =    10      
          
Then          
          
x = critical value =    86.44853627   [ANSWER, 95TH PERCENTILE]