Question

The cholesterol levels of an adult can be described by a normal model with a mean of 187 ​mg/dL and a standard deviation of 28

What percent of adults do you expect to have cholesterol levels over 210 ​mg/dL? (round two decimal places)

​c) What percent of adults do you expect to have cholesterol levels between 150 and 160 mg/dL?(round two decimal places)

d) Estimate the interquartile range of cholesterol levels.

IQR= ____ (round to nearest integer)

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

Answer 1

a)
Here, μ = 187, σ = 28 and x = 210. We need to compute P(X >= 210). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (210 - 187)/28 = 0.82

Therefore,
P(X >= 210) = P(z <= (210 - 187)/28)
= P(z >= 0.82)
= 1 - 0.7939 = 0.2061
= 20.61%

b)

Here, μ = 187, σ = 28, x1 = 150 and x2 = 160. We need to compute P(150<= X <= 160). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (150 - 187)/28 = -1.32
z2 = (160 - 187)/28 = -0.96

Therefore, we get
P(150 <= X <= 160) = P((160 - 187)/28) <= z <= (160 - 187)/28)
= P(-1.32 <= z <= -0.96) = P(z <= -0.96) - P(z <= -1.32)
= 0.1685 - 0.0934
= 0.0751
= 7.51%

d)

z avlue at 25% = -0.67

z = (x - mean)/s
-0.67 = (x - 187)/28

x = -0.67 * 28 + 187
= 168.24

z avlue at 75% = 0.67

z = (x - mean)/s
0.67 = (x - 187)/28

x = 0.67 * 28 + 187
= 205.76

IQR = Q3 - Q1
= 205.76 - 168.24
= 38

e)
z avlue at 15% =1.04

z = (x - mean)/s
1.04 = (x - 187)/28
x = 1.04 * 28 + 187
= 216