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High-density lipoprotein (HDL) is sometimes called the "good cholesterol" because low values are associated with a higher risk of heart disease. According to the American Heart Association, people over the age of 20 years should have at least 40 mg/dL of HDL cholesterol. U.S. women aged 20 and over have a mean HDL of 55 mg/dL with a standard deviation of 15.5 mg/dL. Assume that the distribution is Normal.
what percentage of women have low values of HDL? (40mg/ dL or less)


(Fill in the blank below and round your answer to a whole number.)

________% of women have low values of HDL

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Answer:

17% of women have low values of HDL

Step-by-step explanation:

We need to calculate the z-score of low HDL level in the distribution.

z score can be calculated using the formula

z=[tex]\frac{X-M}{s}[/tex] where

  • X is women's cut-off level for low HDL(40 mg/dL)
  • M is the mean HDL for US women aged 20 and over (55 mg/dL)
  • s is the standard deviation (15.5 mg/dL)

Putting these numbers in the formula, we get

z=[tex]\frac{40-55.5}{15.5}[/tex] = -0.9677

By looking the z table P(Z<−0.9677) =0.1666

Then, in order to find the corresponding percentile we compute:

100×0.1666 = 16.66% ≈ 17%

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