Question

question 3 of 10
according to a health information website, the distribution of adults diastolic blood pressure (in millimeters of mercury) can be modeled by a normal distribution with mean 70 and standard deviation 20. a diastolic blood pressure between 80 and 90 indicates borderline high blood pressure.
what proportion of adults have borderline high blood pressure? round to 4 decimal places.

Explanation:

Step1: Calculate z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu = 70$ (mean) and $\sigma = 20$ (standard deviation).
For $x = 80$, $z_1=\frac{80 - 70}{20}=\frac{10}{20}=0.5$.
For $x = 90$, $z_2=\frac{90 - 70}{20}=\frac{20}{20}=1$.

Step2: Use the standard normal distribution table

We want to find $P(0.5We know that $P(Z < 1)\approx0.8413$ and $P(Z < 0.5)\approx0.6915$.
So $P(0.5 < Z < 1)=P(Z < 1)-P(Z < 0.5)$.
$P(0.5 < Z < 1)=0.8413 - 0.6915=0.1498$.

Answer:

$0.1498$