Question

systolic blood pressure readings for a population of adults are normally distributed with a mean of 125 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 below 155.
click the icon to view the table of z - scores and percentiles.
the z - score is
(type an integer or a decimal.)
the percentage of people with blood pressure readings below 155 is %
(round to two decimal places as needed.)

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x = 155\), \(\mu=125\), and \(\sigma = 15\).

$$z=\frac{155 - 125}{15}=\frac{30}{15}=2$$

Step2: Find the percentage using the z - score table

Looking up the z - score of \(z = 2\) in the standard normal distribution table (z - score and percentile table). The value corresponding to \(z = 2\) is \(0.9772\) or \(97.72\%\)

Answer:

The z - score is \(2\).
The percentage of people with blood pressure readings below \(155\) is \(97.72\%\)