Question

The total cholesterol levels of a sample of men aged​ 35-44 are normally distributed with a mean of 215 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 225 milligrams per deciliter of​ blood?

​(b) If 241 men in the​ 35-44 age group are randomly​ selected, about how many would you expect to have a total cholesterol level greater than 257 milligrams per deciliter of​ blood

Answer 1

Solution :

Given that ,

mean = = 215

standard deviation = = 38.8

(a)

P(x < 225) = P[(x - ) / < (225 - 215) / 38.8]

= P(z < 0.26)

= 0.6026

Probability = 0.6026

(b)

P(x > 257) = 1 - P(x < 257)

= 1 - P[(x - ) / < (257 - 215) / 38.8]

= 1 - P(z < 1.08)

= 0.1401   

Probability = 0.1401

241 * 0.1401 = 34 would you expect .