Question

Too much cholesterol in the blood increases the risk of heart diseases. Young women are generally less afflicted with high cholesterol than other groups. The cholesterol levels for women aged 20 to 34 follow an approximately normal distribution with mean 190 milligrams per deciliter (mg/dl) and standard deviation 41 mg/dl.

(a) Cholesterol levels above 270 mg/dl demand medical attention. What percent of young women have levels above 270 mg/dl?

(b) Levels above 220 mg/dl are considered borderline high. What percent of young women have blood cholesterol between 220 and 270 mg/dl?

	I.	4.2%, 40.23%
	II.	2.56%, 20.71%
	III.	1.34%, 10.25%
	IV.	12.13%, 76.00%

Answer 1

Solution :

Given that ,

mean = = 190

standard deviation = = 41

a. P(x > 270 ) = 1 - p( x< 270 )

=1- p P[(x - ) / < ( 270 - 190) / 41]

=1- P(z < 1.95)

Using z table,

= 1 - 0.9744

= 0.0256

= 2.56%

b. P( 220 < x < 270) = P[(220 - 190)/ 41) < (x - ) /  < (270 - 190) / 41) ]

= P( 0.73 < z < 1.95)

= P(z < 1.95) - P(z < 0.73)

Using z table,

= 0.9744 - 0.7673

= 0.2071

= 20.71%

correct option :- || 2.56% , 20.71%