For the samples of size 36 which sample mean is higher than

For the samples of size 36, which sample mean is higher than 96% of all other sample means?

Please show all work!

Solution

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.96      
          
Then, using table or technology,          
          
z =    1.750686071      
          
As x = u + z * s / sqrt(n)          
          
where          
          
u = mean =    2.26      
z = the critical z score =    1.750686071      
s = standard deviation =    0.28      
n = sample size =    36      
Then          
          
x = critical value =    2.341698683   [ANSWER]