Question

systolic blood pressure readings for a population of adults are normally distributed with a mean of 119 and a standard deviation of 15. (a reading above 140 is considered to be high - blood pressure.) begin by converting the given blood pressure reading into a z - score. then use the accompanying table of z - scores and percentiles to find the percentage of people with blood pressure readings above 128.
click the icon to view the table of z - scores and percentiles.
the z - score is

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x = 128\), \(\mu=119\), and \(\sigma = 15\).

$$
LATEXBLOCK0
$$

Step2: Find the percentage of people with blood pressure readings above 128

Using the standard normal distribution table (z - table), for \(z = 0.6\), the cumulative probability \(P(Z\leq0.6)\) is \(0.7257\).
The probability \(P(Z>0.6)=1 - P(Z\leq0.6)\)

$$
LATEXBLOCK1
$$

Answer:

The z - score is \(0.6\). The percentage of people with blood pressure readings above \(128\) is \(27.43\%\)