Cholesterol levels in the American adult population have app

Cholesterol levels in the American adult population have approximately a bell shaped distribution with a mean 152 and standard deviation 8.9. A \"healthy\" level is one that falls within the range of 95% of all cholesterol levels. What is the largest \"healthy\" cholesterol?

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Solution

Note that              
              
Lower Bound = u - z(alpha/2) * sigma              
Upper Bound = u + z(alpha/2) * sigma              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
u = population mean =    152          
z(alpha/2) = critical z for the confidence interval =    1.959963985          
sigma = population standard deviation =    8.9          
              
              
Thus,              
              
Lower bound =    134.5563205          
Upper bound =    169.4436795          
              
Thus, the confidence interval is              
              
(   134.5563205   ,   169.4436795   )

Hence, the largest healthy cholesterol is 169.4437. [answer]