Question

systolic blood pressure readings for a population of adults are normally distributed with a mean of 125 and a standard deviation of 20. (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 113. click the icon to view the table of z - scores and percentiles. the z - score is - 0.6. (type an integer or a decimal.) the percentage of people with blood pressure readings above 113 is %. (round to two decimal places as needed.)

Explanation:

Step1: Recall z - score and percentile relationship

A z - score of - 0.6 corresponds to a percentile in the z - score table. Looking up the percentile for z=-0.6 in the standard normal distribution table, we find the percentile is 0.2743. This represents the proportion of values below the z - score of - 0.6.

Step2: Calculate proportion above the value

We want the percentage of people with blood - pressure readings above 113 (which has a z - score of - 0.6). The total area under the normal distribution curve is 1. To find the proportion of values above a particular z - score, we use the formula \(P(Z > z)=1 - P(Z < z)\). Since \(P(Z < - 0.6)=0.2743\), then \(P(Z > - 0.6)=1 - 0.2743 = 0.7257\).

Step3: Convert proportion to percentage

To convert the proportion to a percentage, we multiply by 100. So \(0.7257\times100 = 72.57\%\).

Answer:

72.57%