Question

The total cholesterol levels of a sample of men aged​ 35-44 are normally distributed with a mean of 224 milligrams per deciliter and a standard deviation of 37.8 milligrams per deciliter. ​(a) What percent of the men have a total cholesterol level less than 236 milligrams per deciliter of​ blood? ​(b) If 248 men in the​ 35-44 age group are randomly​ selected, about how many would you expect to have a total cholesterol level greater than 254 milligrams per deciliter of​ blood?

Answer 1

Solution :

Given that ,

mean = = 224

standard deviation = = 37.8

P(X< 236) = P[(X- ) / < (236-224) / 37.8]

= P(z < 0.32)

Using z table

= 0.6255

=62.55% percent of the men have a total cholesterol level less than 236 milligrams per deciliter of​ blood

b)

n=248

P(x > 254) = 1 - P(x< 254)

= 1 - P[(x -) / < (254-224) / 37.8]

= 1 - P(z < 0.79)

Using z table

= 1 - 0.7852

= 0.2148

=0.2148 * n

=0.2148*248

=53.2704

answer =53.27