The total cholesterol levels of a sample of men aged 3544 ar

The total cholesterol levels of a sample of men aged 35-44 are normally distributed with a mean of210 milligrams per deciliter and a standard deviation of 37.9 milligrams per deciliter. (a) What percent of the men have a total cholesterol level less than 219 milligrams per deciliter of blood? (b) If 253 men in the 35-44 age group are randomly selected, about how many would you expect to have a total cholesterol level greater than 268 milligrams per deciliter of blood? (a) The percent of the men that have a total cholesterol level less than 219 milligrams per deciliter of blood is %. (b) Of the 253 men selected, would be expected to have a total cholesterol level greater than 268 milligrams per deciliter of blood.

Solution

Normal Distribution
Mean ( u ) =210
Standard Deviation ( sd )=37.9
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X < 219) = (219-210)/37.9
= 9/37.9= 0.2375
= P ( Z <0.2375) From Standard Normal Table
= 0.5939                  

b)
P(X > 268) = (268-210)/37.9/ Sqrt ( 253 )
= 58/2.383= 24.3416
= P ( Z >24.3416) From Standard Normal Table
= 0                  
No, we don\'t have enough evidence that it has more than 268