Question

blood pressure
use the following information to answer the questions:
systolic blood pressure readings for a population of adults are
normally distributed with a mean of 120 and a standard deviation
of 15. (a reading above 140 is considered to be high blood
pressure.)
part b
what percent of people have a blood pressure reading lower
than 165?
a 65%
b 95%
c 97.5%
d 98.5%
e 99.85%

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x - \mu}{\sigma}\), where \(x = 165\), \(\mu=120\), and \(\sigma = 15\).

$$z=\frac{165 - 120}{15}=\frac{45}{15}=3$$

Step2: Find the percentage using the standard normal distribution table

We want to find \(P(X\lt165)\), which is equivalent to \(P(Z\lt3)\) in the standard normal distribution.
From the standard normal distribution table, \(P(Z\lt3)=0.9987\) or \(99.87\%\approx99.85\%\)

Answer:

E. 99.85%