Question

systolic blood pressure readings for a population of adults are normally distributed with a mean of 124 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 130. click the icon to view the table of z - scores and percentiles. the z - score is 0.4 (type an integer or a decimal.) the percentage of people with blood pressure readings above 130 is % (round to two decimal places as needed.)

Explanation:

Step1: Find the percentile corresponding to z - score

The z - score is \(z = 0.4\). From the standard normal distribution table (z - score and percentile table), the percentile corresponding to \(z=0.4\) is \(65.54\%\). This means that approximately \(65.54\%\) of the data lies to the left of the value with \(z = 0.4\).

Step2: Calculate the percentage of data above the value

Since the total percentage of data in a distribution is \(100\%\), the percentage of data above the value (right - tailed probability) is \(P(X>130)=100\%-\text{Percentile of }z = 0.4\).

Substitute the percentile value: \(P(X > 130)=100 - 65.54\)

Answer:

\(34.46\%\)