Question

Please show work.

Total serum cholesterol levels for individuals 65 years of age and older are assumed to follow a normal distribution, with a mean of 182 mg/dL and a standard deviation of 14.7 mg/dL.

10) What proportion of these individuals have cholesterol levels of 175 mg/dL or more?

11) What proportion of these individuals have cholesterol levels between 150 mg/dL and 175 mg/dL?

12) If the top 10% of the cholesterol levels are assumed to be abnormally high, what is the upper limit of the normal range? (Hint: use NORMINV)

Answer 1

Solution :

Given that ,

10) P(x 175) = 1 - P(x   175 )

= 1 - P[(x - ) / (175 - 182) / 14.7]

= 1 -  P(z - 0.48)

= 1 - 0.3156

= 0.6844

11) P( 150 < x < 175 ) = P[(150 - 182) / 14.7 ) < (x - ) /  < (175 - 182) / 14.7) ]

= P( - 2.18 < z < -0.48)

= P(z < -0.48) - P(z < - 2.18 )

Using z table,

= 0.3156 - 0.0146

= 0.3010

12) Using standard normal table,

P(Z > z) =10%

= 1 - P(Z < z) = 0.10  

= P(Z < z) = 1 - 0.10

= P(Z < z ) = 0.90

= P(Z < 1.28) = 0.90  

z = 1.28

Using z-score formula,

x = z * +

x = 1.28 * 14.7 + 182

x = 200.82