Question

5. It is reported that the cholesterol level for U. S. women ages between 50 and 59 yields a mean milligrams per deciliter and a standard deviation milligrams 2288.43per deciliter. (Assume the distribution is Normally Distributed)

a) What percentage of women has a total cholesterol level less than 239 milligrams per deciliter of blood?

b) If 200 U. S. women in the 50-59 age group were randomly selected, about how many would you expect to have a total cholesterol level greater than 200 milligrams per deciliter of blood?

Answer 1

Solution :

Given that,

mean = = 228

standard deviation = = 8.43

a ) P( x < 239 )

P ( x - / ) < ( 239 - 228 / 8.43)

P ( z < 11 / 8.43 )

P ( z < 1.30)

=0.9032

Probability = 0.9032

90.32% of women has a total cholesterol level less than 239 milligrams per deciliter of blood

b ) P (x > 200 )

= 1 - P (x < 200 )

= 1 - P ( x -  / ) < ( 200 - 228 / 8.43)

= 1 - P ( z <- 28 / 8.43 )

= 1 - P ( z < -3.32)

Using z table

= 1 - 0.0005

= 0.9995

Probability =0.9995

N = 200 * 0.9995 = 199.9 milligrams expect to have a total cholesterol level greater than 200 milligrams per deciliter of blood