x is a normally distributed random variable with a mean of 8 and a standard devi

Question

x is a normally distributed random variable with a mean of 8 and a standard deviation of 1.5. find the value of x for which 70.54% of the area under the distribution curve lies to the right of it x is a normally distributed random variable with a mean of 8 and a standard deviation of 1.5. find the value of x for which 70.54% of the area under the distribution curve lies to the right of it x is a normally distributed random variable with a mean of 8 and a standard deviation of 1.5. find the value of x for which 70.54% of the area under the distribution curve lies to the right of it

Explanation / Answer

First, we get the z score from the given left tailed area. As          
          
Left tailed area = 1 - 0.7054 =   0.2946      
          
Then, using table or technology,          
          
z =    -0.539995697      
          
As x = u + z * s,          
          
where          
          
u = mean =    8      
z = the critical z score =    -0.539995697      
s = standard deviation =    1.5      
          
Then          
          
x = critical value =    7.190006455   [ANSWER]  

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