Question

blood pressure use the following information to answer the questions: systolic blood pressure readings for a population of adults are normally distributed with a mean of 120 and a standard deviation of 15. (a reading above 140 is considered to be high blood pressure.) part b what percent of people have a blood pressure reading lower than 165? a 65% b 95% c 97.5% d 98.5% e 99.85%

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(x = 165\), \(\mu=120\), and \(\sigma = 15\).

$$z=\frac{165 - 120}{15}=\frac{45}{15}=3$$

Step2: Use the standard normal distribution property

In a standard normal distribution (\(N(0,1)\)), about \(99.7\%\) of the data lies within \(z=- 3\) and \(z = 3\). The proportion of data to the left of \(z = 3\) can be found using the cumulative distribution function of the standard normal distribution. The cumulative probability \(P(Z<3)\) is approximately \(0.9985\) or \(99.85\%\) (from the standard normal table or using a calculator with a normal - distribution function).

Answer:

E. \(99.85\%\)