6.32 Serum Cholesterol Levels. According to the National
Health and Nutrition Examination Survey, published by the Na-
tional Center for Health Statistics, the serum (noncellular portion
of blood) total cholesterol level of U.S. females 20 years old or
older is normally distributed with a mean of 206 mg/dL (mil-
ligrams per deciliter) and a standard deviation of 44.7 mg/dL.
Let x denote serum total cholesterol level for U.S. females
20 years old or older.
a. Sketch the distribution of the variable x.
b. Obtain the standardized version, z, of x.
c. Identify and sketch the distribution of z.
d. The percentage of U.S. females 20 years old or older who
have a serum total cholesterol level between 150 mg/dL
and 250 mg/dL is equal to the area under the standard normal
curve between
and
e. The percentage of U.S. females 20 years old or older who have
a serum total cholesterol level below 220 mg/dL is equal to the
area under the standard normal curve that lies to the
of
b