#### The distribution of blood cholesterol levels in 14-year-old boys is roughly normal; the mean is 165 milligrams of cholesterol per deciliter of blood and the standard deviation is 30. a. What Proportion.

- Proportion of 14-year-old boys have level between 120 and 200 is 0.8122.
- Proportion have level over 20 is 1.
- Proportions have level over 160 in sample of 200 boys is 0.9908.
- Sample 500 boys, proportion have level over 170 is 0.0001.
- Level separates the boys who have level in the highest 70% from those in the lowest 30% is 149.268.

Given,

*μ* = 165

*σ* = 30

1) Proportion of 14-year-old boys have level between 120 and 200 :

p(120 < x < 200) = p(120-165/30 < z < 200 – 165 / 30)

p(120 < x < 200) = p(-1.5 < z < 1.17)

p(120 < x < 200) = 0.8122

2) Proportion have level over 20,

p(x > 20) = p(z > 20 – 165/30)

p(x > 20) = 1

3) Proportions have level over 160 in sample of 200 boys,

*μ* = 165

*σ* = 30

n = 200

p(x>160) =

p(x>160) = p(z > 2.36)

= 0.9908

4) Sample 500 boys, proportion have level over 170

p(x>170) =

p(x>160) = p(z > 3.73)

= 0.0001

5) Level separates the boys who have level in the highest 70% from those in the lowest 30%,

= 30%

= 0.03

p(z < -0.524) = 0.30

x =

x = 165 + (30*-0.524)

x = 149.268

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