Chapter 2.2, Problem 3.2CYU

To determine

To find: The percent of 14-year old boys have the blood cholesterol level between 200 and 240 mg/dl.

Answer to Problem 3.2CYU

The percentage is 14.88%

Explanation of Solution

Given:

Population mean $\left(\mu \right)=170$

Population standard deviation $\left(\sigma \right)=30$

Calculation:

Consider, X be the random variable that is following the normal distribution.

The percentage is computed as:

  $\begin{array}{c}P\left(200<X<240\right)=P\left(\frac{200-\mu }{\sigma }<\frac{x-\mu }{\sigma }<\frac{240-\mu }{\sigma }\right)\\ =P\left(\frac{200-170}{30}<Z<\frac{240-170}{30}\right)\\ =P\left(1<Z<2.33\right)\\ =0.1488\end{array}$

The figure could be constructed as:

Thus, the required percentage is 14.88%.