As reported by the US National Center for Health Statistics, the mean serum high

Question

As reported by the US National Center for Health Statistics, the mean serum high-density-lipoprotein (HDL) cholesterol of females 20-29 years old is 53 . If serum HDL cholesterol is normally distributed with 12 . (Statistics: Informed Decisions Using Data, Michael Sullivan, III)

4. If one 20-29 year old female is randomly selected, what is the probability that her HDL cholesterol is between (2pt) 40 and 60?

5. If one 20-29 year old female is randomly selected, what is the probability that her HDL cholesterol is greater (2pt) than 50?

6. The 80th percentile of HDL cholesterol of females 20-29 years old is ____________ . (3pt) The following picture might be helpful:

Explanation / Answer

Solution:- Given mean = 53 ,sd = 12

4. P(40 < x < 60) = P( (40 - 53)/12 < Z < (60 - 53)/12 )
= P( -1.0833 < Z < 0.5833 )
= 0.5789

5 . P(X > 50) = P(Z > (50 - 53)/12)
= P(Z > -0.25)
= P (Z < 0.25 )
= 0.5987

6. (X - 53)/12 = -0.8416
X - 53 = -0.8416*12
X = 53 - (0.8416*12)
X = 42.9008

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