The distribution of blood cholesterol levels in 14-year-old boys.

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) = $\mathrm{p}(\mathrm{X}-\mu / \sigma / \sqrt{n}>160-165 / 30 / \sqrt{ } 200)$

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

= 0.9908

4) Sample 500 boys, proportion have level over 170

p(x>170) = $\mathrm{p}(\mathrm{X}-\mu / \sigma / \sqrt{n}>170-165 / 30 / \sqrt{ } 500)$

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%,

$\mathrm{p}\left(z<z_p\right)=30 \%$ = 30%

= 0.03

p(z < -0.524) = 0.30

x = $\mathrm{X}=\mu+z_p * \sigma$

x = 165 + (30*-0.524)

x = 149.268

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