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 a
what is the z - score of a person with a blood pressure reading of 165?
a 1.5
b 2
c 2.66
d 3
e 5
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 for Part B

Using the standard normal distribution table (or the empirical rule extended for \(z = 3\)). The area to the left of \(z = 3\) is \(P(Z<3)\).
From the standard normal table, \(P(Z < 3)=0.9987\approx99.85\%\)

Answer:

Part A: D. 3
Part B: E. 99.85%