Question

Blood pressure Refer to Exercise $56$ According to the same health information website, diastolic blood pressure between $80$ and $90$ indicates borderline high blood pressure. About what percent of adults have borderline high blood pressure?

Short answer

Around $14.98\%$ of the adults have borderline high blood pressure.

Step-by-step solution

Given information

Daily allowance,$x=80or90$

Mean,$\mu =70$

Standard deviation,$\sigma =20$

Concept

The formula used:$z=\frac{x-\mu }{\sigma }$

Calculation

Calculate the $z-$ score,

$z=\frac{x-\mu }{\sigma }=\frac{80-70}{20}=0.50$

or

$z=\frac{x-\mu }{\sigma }=\frac{90-70}{20}=1.00$

To find the equivalent probability, use the normal probability table in the appendix.

In the typical normal probability table for $P(z<0.50)$, look at the row that starts with $0.5$ and the column that starts with$.00$

or

The conventional normal probability table for $P(z<1.00)$has a row that starts with 1.0 and a column that starts with.00.

$$\begin{gathered} P(80<x<90)=P(0.50<z<1.00) \\ =P(z<1.00)-P(z<0.50) \\ =0.8413-0.6915 \\ =0.1498 \\ =14.98\% \end{gathered}$$

Therefore,

Approximately $14.98$ percent of adults have a diastolic blood pressure of $80$ to $90$ which is considered borderline high blood pressure.