Chapter 2.2, Problem 56E

To determine

Proportion of adults having very high blood pressure according to the criterion.

Answer to Problem 56E

Around 6.68% of the adults have very high blood pressure according to the criterion.

Explanation of Solution

Given information:

Diastolic pressure value, $x=100$

Mean, $\mu =70$

Standard deviation, $\sigma =20$

Calculations:

Calculate the Z − score,

  $z=\frac{x-\mu }{\sigma }=\frac{100-70}{20}=1.50$

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

See the row that starts with 1.5 and the column that starts with .00 of the standard normal probability table for $P\left(z<0.80\right)$ .

  $\begin{array}{l}P\left(x>100\right)=P\left(z<1.50\right)\\ =1-P\left(z>0.80\right)\\ =1-0.9332\\ =0.0668\\ =6.68\%\end{array}$

Therefore,

Around 6.68% of the adults have a diastolic pressure exceeding 100, that has been classified as very high blood pressure.