4.10 find the sd. cholesterol levels for women aged 20 to 34 follow an approximately normal distribution with mean 185 milligrams per deciliter (mg/dl). women with cholesterol levels above 220 mg/dl are con- sidered to have high cholesterol and about 18.5% of women fall into this category. what is the standard deviation of the distribution of cholesterol levels for women aged 20 to 34?

Standard deviation = 38.89 ≈ 39 mg/dl

Step-by-step explanation:

Data provided in the question:

Mean of the normal distribution = 185 milligrams per deciliter

Let X denote the cholesterol level of women aged 20 to 34 (in mg/dl)

Therefore,

P( X > 220 ) = 18.5% = 0.185

Now,

P( X > 220 ) =

Now,

From the standard Z table = 0.185

we have Z = 0.90

Thus,

= 0.90

or

= 0.90

or

Standard deviation =

or

Standard deviation = 38.89 ≈ 39 mg/dl

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