The cholesterol levels of an adult can be described by a nor

The cholesterol levels of an adult can be described by a normal model with a mean of 198 mg/dL and a standard deviation of 29.

a) What percent of adults do you expect to have cholesterol levels over 220mg/dL?

b)What percent of adults do you expect to have cholesterol levels between 170 and 180 mg/dL?

c) Estimate the interquartile range of cholesterol levels

IQR= ___ mg/dL

d) Above what value of the highest 15% of adults\' cholesterol levels?

Solution

A)
? = 180
? = 24
standardize x to z = (x - ?) / ?
P(x > 200) = P( z > (200-180) / 24)
= P(z > 0.5) = 0.3085 (30.85 percent)
(From Normal probability table)

B)
? = 180
? = 24
standardize x to z = (x - ?) / ?
P( 150 < x < 170) = P[( 150 - 180) / 24 < Z < ( 170 - 180) / 24]
P( -1.5833 < Z < -0.75) = P( z < -0.75) - P( z < -1.5833) = 0.2266 - 0.0571 = 0.1695 = 16.95 percent
(From Normal probability table)

d)

From the standard normal distribution table, the z corresponding to the top 15% is
P( z > 1.04 ) = 0.15
z = (x - ?) / ?
1.04 = (x-180) /24
x = 180 + (1.04)(24)
x = 212.96 mg/dL

c)
From the normal table, P( z < -0.67 ) = 0.25
P( z < -0.67 ) = 0.25
z = (x - ?) / ?
-0.67 = (x-180) /24
x = 180 - (0.67)(24)
x = 171.92 mg/dL -----> Q1

From the normal table, P( z < 0.67 ) = 0.75
P( z < 0.67 ) = 0.75
z = (x - ?) / ?
0.67 = (x-180) /24
x = 180 + (0.67)(24)
x = 204.88 mg/dL -----> Q3

Q3-Q1 = 32.16 (IQR)