Question

systolic blood pressure readings for a population of adults are normally distributed with a mean of 120 and a standard deviation of 10. (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 144.
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 144 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 \(x = 144\), \(\mu=120\), and \(\sigma = 10\).

$$z=\frac{144 - 120}{10}=\frac{24}{10}=2.4$$

Step2: Find the percentage using the z - score

Looking up the z - score of \(z = 2.4\) in the standard normal distribution table (z - score and percentile table). The value corresponding to \(z = 2.4\) gives the proportion of data to the left of \(z = 2.4\). From the standard normal table, the area to the left of \(z=2.4\) is \(0.9918\) or \(99.18\%\)

Answer:

The z - score is \(2.4\).
The percentage of people with blood pressure readings below \(144\) is \(99.18\%\)