The blood cholesterol levels of women aged 20 to 34 are approximately normally d

Question

The blood cholesterol levels of women aged 20 to 34 are approximately normally distributed with mean mu =185 milligrams per deciliter and standard deviation sigma = 39 mg/dl. a) What percentage of the women in this age group have a cholesterol level less than 185 mg/dL? b) If high cholesterol is defined to be a level of 240 mg/dL or above, what percentage of women in this age group have high cholesterol? c) Borderline high cholesterol is defined to be a level between 200 and 240 mg/dL. What percentage of women in this age group have borderline high cholesterol?

Explanation / Answer

The blood cholesterol levels of women aged 20 to 34 are approximately normally distributed with mean mu =185 milligrams per deciliter and standard deviation sigma = 39 mg/dl. LET US PUT MEAN = M = 185...........................STD.DEVN.= S = 39 .... a) What percentage of the women in this age group have a cholesterol level less than 185 mg/dL? THAT IS ..... Z < =[X-M] / S = [185-185]/39 < = 0 SO WE WANT THE AREA UNDER THE PROBABILITY CURVE FROM Z = 0 TO - INFINITY ..FROM TABLES .. THE AREA = 0.5 ................................. THAT IS 50% OF THE POPULATION WILL BE IN THIS GROUP ...... b) If high cholesterol is defined to be a level of 240 mg/dL or above, what percentage of women in this age group have high cholesterol? THAT IS .... Z > = [240-185] / 39 = 1.41. SO WE WANT THE AREA UNDER THE PROBABILITY CURVE FROM Z = 1.4103 TO INFINITY ..FROM TABLES .. THE AREA = 0.5000-0.4207 = 0.0793 THAT IS 7.93 % OF THE POPULATION WILL BE IN THIS GROUP . c) Borderline high cholesterol is defined to be a level between 200 and 240 mg/dL. What percentage of women in this age group have borderline high cholesterol? THAT IS [200-185] / 39

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