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 171 and standard deviation 6.4. A \"healthy\" level is one that falls within the range of 95% of all cholesterol levels. What is the largest \"healthy\" cholesterol?

Solution

P ( Z < x ) = 0.95
Value of z to the cumulative probability of 0.95 from normal table is 1.645
P( x-u/s.d < x - 171/6.4 ) = 0.95
That is, ( x - 171/6.4 ) = 1.64
--> x = 1.64 * 6.4 + 171 = 181.528 ~ 182 is the largest