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 deviations of 36.8 milligrams per deciliter.

(a) What percent of the men have a total cholesterol level less than 235 milligrams per deciliter of blood?

(b) If 245 men in the 35-44 are group are randomly selected, about how many would you expect to have a total cholesterol level greater than 252 milligrams per deciliter of blood?

Answer 1

Solution :

(a)

P(x < 235) = P[(x - ) / < (235 - 222) / 36.8]

= P(z < 0.35)

= 0.6368

Answer = 63.38%

(b)

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

= 1 - P[(x - ) / < (252 - 222) / 36.8]

= 1 - P(z < 0.82)

= 1 - 0.7939

= 0.2061

Answer = 0.2061 * 245 = 50.5

50.5 would be expect