Question

The total cholesterol levels of a sample of men aged​ 35-44 are normally distributed with a mean of

200 milligrams per deciliter and a standard deviation of 38.8 milligrams per deciliter.

​(a) What percent of the men have a total cholesterol level less than 236 milligrams per deciliter of​ blood?

​(b) If 247 men in the​ 35-44 age group are randomly​ selected, about how many would you expect to have a total cholesterol level greater than

255 milligrams per deciliter of​ blood?

Answers...

a) The percent of the men that have a total cholesterol level less than 236 milligrams per deciliter of blood is ___

b) Of the men selected, ___ would be expected to have a total cholesterol level greater than 255 milligrams per decliliter of blood.

Answer 1

Solution :

Given that ,

mean = = 200

standard deviation = = 38.8

(a)

P(x < 236) = P((x - ) / < (236 - 200) / 38.8)

= P(z < 0.93)

Using standard normal table,

P(x < 236) = 0.8238

The percent of the men that have a total cholesterol level less than 236 milligrams per

deciliter of blood is 82.38 .

(b)

P(x < 255) = P((x - ) / < (255 - 200) / 38.8)

= P(z < 1.42)

Using standard normal table,

P(x < 255) = 0.9222

So , 247 * 0.9222 = 227.78 = 228

Of the men selected, 228 would be expected to have a total cholesterol

level greater than 255 milligrams per decliliter of blood .