Question

The blood cholesterol levels of men aged 55 to 64 are approximately normal with mean 222 mg/dl and standard deviation 37 mg/dl. What range of values corresponds to the 10% highest cholesterol levels? A) > 175 B) > 247 C) > 269 D) > 288 Gown Z Area Area left right 90% 10% 37 1.28 148 296 111 333 185 222 259 Cholesterol level (mg/dl) DEEP FRIED BUTTER

Answer 1

Let X denote the blood cholesterol levels of men aged 55 to 64 are approximately normal with mean 222 mg/dl and standard deviation 37 mg/dl.

$So, Z = \frac{X-\mu}{\sigma} =\frac{X-222}{37} \sim N(0,1)$

We need to find the range of values corresponds to the 10% highest cholesterol levels,

So, we want to find 'x; such that

$P[X> x] = 0.1 \Rightarrow P[\frac{X-222}{37}>\frac{x-222}{37}]=0.1$

$P[Z >\frac{x-22}{37}]=0.1$

$\Rightarrow 1 - P[Z <\frac{x-22}{37}]=0.1$

T 0 22 -) = 0.9 37

$\Rightarrow \frac{x-22}{37}=\Phi^{-1}(0.9)=1.28$

$\Rightarrow x= 269$ (approx.)

So the answer is (C)