Question

The total cholesterol levels of a sample of men aged​ 35-44 are normally distributed with a mean of 222 milligrams per deciliter and a standard deviation of 38.1 milligrams per deciliter.

(a) The percent of the men that have a total cholesterol level less than 228 milligrams per deciliter of blood is what ​%. ​(Round to two decimal places as​ needed.

(b) of the 245 men selected____would be expected to have a total cholesterol level greater than 252 milligrams per deciliter of blood

Answer 1

Solution :

Given that ,

mean = = 222

standard deviation = = 38.1

P(x < 228) = P[(x - ) / < (228 - 222) / 38.1]

= P(z < 0.16)

= 0.5636

(b)

P(x > 252) = 1 - P(x < 252)

= 1 - P[(x - ) / < (252 - 222) / 38.1]

= 1 - P(z < 0.78)

= 0.2177

245 * 0.2177 = 53.3

Of the 245 men selected 53.3 would be expected to have a total cholesterol level greater than 252 milligrams per

deciliter of blood .