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Too much cholesterol in the blood increases the risk of heart disease. The cholesterol levels of young women age 20 to 34 have an approximate Normal distribution with mean 185 milligrams per deciliter (mg/dL) and standard deviation
39mg//dL.
About what percent of young women in this age group will have cholesterol levels less than
150mg//dL ?

82%

90%

18%

Too much cholesterol in the blood increases the risk of heart disease. The cholesterol levels of young women age $20$ to $34$ have an approximate Normal distribution with mean $185$ milligrams per deciliter (mg/dL) and standard deviation $39 \mathrm{mg} / \mathrm{dL}$ . $\newline$ About what percent of young women in this age group will have cholesterol levels less than $150 \mathrm{mg} / \mathrm{dL}$ ? $\newline$ $82 \%$ $\newline$ $90 \%$ $\newline$ $18 \%$

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Interpret confidence intervals for population means

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Q. Too much cholesterol in the blood increases the risk of heart disease. The cholesterol levels of young women age

20

to

34

have an approximate Normal distribution with mean

185

milligrams per deciliter (mg/dL) and standard deviation

39 \mathrm{mg} / \mathrm{dL}

.

\newline

About what percent of young women in this age group will have cholesterol levels less than

150 \mathrm{mg} / \mathrm{dL}

?

\newline

82 \%

\newline

90 \%

\newline

18 \%

Identify parameters: Identify the parameters of the normal distribution. $\newline$ Mean $\mu$ = $185$ mg/dL $\newline$ Standard Deviation $\sigma$ = $39$ mg/dL $\newline$ We need to find the probability that cholesterol levels are less than $150$ mg/dL.
Calculate Z-score: Calculate the Z-score for $150\,\text{mg/dL}$ . $\newline$ $Z = \frac{X - \mu}{\sigma}$ $\newline$ $Z = \frac{150 - 185}{39}$ $\newline$ $Z = \frac{-35}{39}$ $\newline$ $Z \approx -0.897$
Use Z-score: Use the Z-score to find the corresponding percentile from the standard normal distribution table. Looking up $Z = -0.897$ , we find that the percentile is approximately $18\%$ .

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