Chapter 12.5, Problem 11PPS

a)

To determine

To find : Percent of males have cholesterol below $\text{151}\text{.7}\text{.}$

Answer to Problem 11PPS

  $\text{50\%}$

Explanation of Solution

GivenInformation :

Cholesterol level for adult males of a specific racial group is normally distributed with a mean of $\text{158}\text{.3}$ and Standard deviation of $\text{6}\text{.6}$.

Calculation:

Using Empirical Rule,

  $\begin{array}{l}\text{151}\text{.7 is at 1}\sigma \text{, 34\% values}\\ \text{145}\text{.1 is at 2}\sigma \text{, 13}\text{.5\% values}\\ \text{145}\text{.1 is at 3}\sigma \text{, 2}\text{.5\% values}\\ p(x<151.7)=34+13.5+2.5=50\%\end{array}$

  

b)

To determine

  $\text{How many of 900 men in a study have chlesterol between 145}\text{.1 and 171}\text{.5 ?}$

Answer to Problem 11PPS

  $\text{873}$

Explanation of Solution

Calculation:

  $\begin{array}{l}\text{Using Empirical Rule}\\ \text{145}\text{.1 is at 2}\sigma \text{, 13}\text{.5\%}\\ \text{151}\text{.7 is at 1}\sigma \text{, 34\%}\\ \text{158}\text{.3 is mean, 34\%}\\ \text{164}\text{.9 is at 1}\sigma \text{, 13}\text{.5\%}\\ \text{171}\text{.5 is at 2}\sigma \text{, 2\%}\\ P(145.1<x<171.5)=13.5+34+34+13.5+2=97\%\\ \text{Since, 97\% }\times \text{ 900 = 873,}\\ \text{mens have cholesterol between 145}\text{.1 and 171}\text{.5}\text{.}\end{array}$