Question

systolic blood pressure readings for a population of adults are normally distributed with a mean of 115 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 105. click the icon to view the table of z - scores and percentiles the z - score is - 0.5 (type an integer or a decimal.) the percentage of people with blood pressure readings above 105 is % (round to two decimal places as needed )

Explanation:

Step1: Find the percentile for \(z = - 0.5\)

Using the standard normal distribution table (z - score table), for \(z=-0.5\), the cumulative probability \(P(Z\leq - 0.5)\) is \(0.3085\)

Step2: Calculate the percentage of people with blood pressure above \(105\)

We know that \(P(X > 105)=1 - P(X\leq105)\). Since \(z=\frac{X-\mu}{\sigma}\) and we found \(P(Z\leq - 0.5) = 0.3085\) (where \(X = 105,\mu=115,\sigma = 20\)), then \(P(X>105)=1 - 0.3085\)

$$1-0.3085=0.6915$$

Answer:

\(69.15\%\)