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The cholesterol levels of an adult can be described by a normal model with a mean...

The cholesterol levels of an adult can be described by a normal model with a mean of 185 ​mg/dL and a standard deviation of 28 .

The cholesterol levels of an adult can be described by a normal model with a mean of

185

​mg/dL and a standard deviation of

28

.

​a) Draw and label the normal model.

A.

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A bell-shaped curve with horizontal axis from less than 101 to 269 plus in intervals of 28 begins just above the horizontal axis, increases at an increasing and then decreasing rate to its maximum at 185, and decreases at an increasing and then decreasing rate approaching the horizontal axis. The curve is symmetric. The area below the curve is subdivided into regions by the intervals and labeled as follows: from 157 to 213, "68%"; from 129 to 241, "95%"; from 101 to 269, "99.7%."

B.

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A bell-shaped curve with horizontal axis from less than 17 to 353 plus in intervals of 56 begins just above the horizontal axis, increases at an increasing and then decreasing rate to its maximum at 185, and decreases at an increasing and then decreasing rate approaching the horizontal axis. The curve is symmetric. The area below the curve is subdivided into regions by the intervals and labeled as follows: from 129 to 241, "68%"; from 73 to 297, "95%"; from 17 to 353, "99.7%."

C.

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A bell-shaped curve with horizontal axis from less than 143 to 227 plus begins just above the horizontal axis, increases at an increasing and then decreasing rate to its maximum at 185, and decreases at an increasing and then decreasing rate approaching the horizontal axis. The curve is symmetric. The seven equally spaced horizontal axis labels are as follows, listed here from left to right: 143, 157, 171, 185, 199, 213, 227. The area below the curve is subdivided into regions by the intervals and labeled as follows: from 171 to 199, "68%"; from 157 to 213, "95%"; from 143 to 227, "99.7%."

​b) What percent of adults do you expect to have cholesterol levels over 210 mg/dL?

​c) What percent of adults do you expect to have cholesterol levels between 150 and 180 mg/dL?

​d) Estimate the interquartile range of cholesterol levels.

IQRequals

​(Round to the nearest integer as​ needed.)

​e) Above what value are the highest​ 15% of​ adults' cholesterol​ levels?

​(Round to the nearest integer as​ nee

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

(a) μ = 185, σ = 28

(b) z = (x - μ)/σ

z = (210 - 185)/28 = 0.8929

P(x > 210) = P(z > 0.8929) = 0.1860 (18.6%)

(c) z1 = (150 - 185)/28 = -1.25 and z2 = (180 - 185)/28 = -0.1786

P(150 < x < 180) = P(-1.25 < z < -0.1786) = 0.3235

(d) Middle 75% of the data is contained between z = ± 1.1503

x1 = μ + z1 * σ = 185 - 1.1503 * 28 = 152.79 and x2 = μ + z2 * σ = 185 + 1.1503 * 28 = 217.21

IQR = 217.21 - 152.79 = 64.42

(e) z- score = 1.0364

x = μ + z * σ = 185 + 1.0364 * 28 = 214.02

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