Chapter 3, Problem 31E

(a)

To determine

To find: the marginal distribution of blood pressure level.

Explanation of Solution

Given:

	under 30	30 to 39	over 50
Low	27	37	31
Normal	48	91	93
High	23	51	73

Calculation:

The marginal distribution

“Low” level blood pressure:

  $\begin{array}{c}=\frac{\text{total number of employees with low blood pressure}}{\text{ Total number of employees in survey }}\\ =\frac{95}{474}\times 100\\ =0.20\times 100\\ =20\%\end{array}$

Similarly, for other levels of blood pressures

The marginal distribution of blood pressure level

Blood Pressure		Marginal distribution
	Low	$\frac{95}{474}\times 100=20.0\%$
	Normal	$\frac{232}{474}\times 100=48.9\%$
	High	$\frac{147}{474}\times 100=31.0\%$

(b)

To determine

To find: the conditional distribution of blood pressure level within each age group.

Explanation of Solution

Given:

	under 30	30 to 39	over 50
Low	27	37	31
Normal	48	91	93
High	23	51	73

Calculation:

Calculate the conditional distribution if blood pressure level within each age group.

Consider age Under 30.

Conditional distribution of low blood pressure level

  $\begin{array}{c}=\frac{\text{Number of persons who are under age 30 with low blood level}}{\text{ Total number of persons in the age group of under 30 }}\\ =\frac{27}{98}\times 100\\ =27.6\%\end{array}$

Similarly, for all levels within every age group

The conditional distribution of blood pressure level within each age group:

Blood pressure	Age
		Under 30	30-49	Over 50
	Low	$\frac{27}{98}\times 100=27.6\%$	$\frac{37}{179}\times 100=20.7\%$	$\frac{31}{197}\times 100=15.7\%$
	Normal	$\frac{48}{98}\times 100=49.0\%$	$\frac{91}{179}\times 100=50.8\%$	$\frac{93}{197}\times 100=47.2\%$
	High	$\frac{23}{98}\times 100=23.5\%$	$\frac{51}{179}\times 100=28.5\%$	$\frac{73}{197}\times 100=37.1\%$

(c)

To determine

To find: the comparison these distributions with a segmented bar graph.

Explanation of Solution

Given:

	under 30	30 to 39	over 50
Low	27	37	31
Normal	48	91	93
High	23	51	73

Graph:

  

This is the required graph of the comparison these distributions with a segmented bar graph.

(d)

To determine

To Explain: the brief description of the association between blood pressure and age.

Explanation of Solution

Given:

	under 30	30 to 39	over 50
Low	27	37	31
Normal	48	91	93
High	23	51	73

Yes, there is an association between blood pressure and age among these employees. As the age of the employee increases, percent of employee with high blood pressure increases. And among over 50 employees, there is less employees with low blood pressure.

(e)

To determine

To Explain: that people’s blood pressure increases as they age.

Explanation of Solution

Given:

	under 30	30 to 39	over 50
Low	27	37	31
Normal	48	91	93
High	23	51	73

No, it does not represent that the people blood pressure increase with age. But it shows that in the peoples whose age over 50 chances of high blood pressure increases.