10. The distribution of cholesterol levels in teenage boys is approximately norm

Question

10. The distribution of cholesterol levels in teenage boys is approximately normal wit h a mean of 1 70 and a standard deviation of 30 (Source: u.S. National Center for Health Statistics). Levels above 200 warrant attention. (show all work) What is the probability that a teenage boy has a cholesterol level greater than 200? What is the probability a teenage boy has a cholesterol level between 165 and 225? Assume that a pediatrician's office has 125 teenage boys as patients, how many of these boys will have cholesterol levels below 160? a) b) c)

Explanation / Answer

10.

NORMAL DISTRIBUTION
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 170
standard Deviation ( sd )= 30

a.
probability that a teenege boy has a cholestrol level greater than 200
P(X > 200) = (200-170)/30
= 30/30 = 1
= P ( Z >1) From Standard Normal Table
= 0.1587

b.
probability that a teenege boy has cholestrol between 165 and 225
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 165) = (165-170)/30
= -5/30 = -0.1667
= P ( Z <-0.1667) From Standard Normal Table
= 0.4338
P(X < 225) = (225-170)/30
= 55/30 = 1.8333
= P ( Z <1.8333) From Standard Normal Table
= 0.9666
P(165 < X < 225) = 0.9666-0.4338 = 0.5328

c.
assume that pedestrians office has 125 teenege boys as patients, how many of these boys cholestrol levels less than 160
P(X < 160) = (160-170)/30
= -10/30= -0.3333
= P ( Z <-0.3333) From Standard Normal Table
= 0.3694
= 36.94% of 125 boys = 46.175 approximate 46 boys

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