Question

According to a recent poll cholesterol levels in healthy adults are right skewed with a mean of 209 mg/dL and a standard deviation of 35 mg/dL. A random sample of 42 healthy adults is selected. What is the value of the sample mean cholesterol level such that 92.5% of sample mean values are below this level?

a. 158.6

b. 216.777

c. 201.223

d. 259.4

Answer 1

Solution :

Given that ,

mean = = 209

standard deviation = = 35

n = 42

= = 209 and

= / n = 35 / 42 = 5.4006

The z - distribution of the 92.5% is,

P( Z < z ) = 92.5 %

P( Z < z ) = 0.925

P( Z < 1.44 ) = 0.925

z = 1.44

Using z - score formula,

= z * +

= 1.44 * 5.4006 + 209  

= 216.777

Option b is correct.