Chapter 2.2, Problem 58E

To determine

Percentage of adults having borderline high blood pressure.

Answer to Problem 58E

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

Explanation of Solution

Given information:

Daily allowance, $x=80\text{or 90}$

Mean, $\mu =70$

Standard deviation, $\sigma =20$

Calculations:

Calculate the z − score,

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

Or

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

Use normal probability table in the appendix, to find the corresponding probability.

See the row that starts with 0.5 and the column that starts with .00 of the standard normal probability table for $P\left(z<0.50\right)$ .

Or

See the row that starts with 1.0 and the column that starts with .00 of the standard normal probability table for $P\left(z<1.00\right)$ .

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

Therefore,

Around 14.98% of the adults have a diastolic blood pressure between 80 and 90 that has been indicated as a borderline high blood pressure.