Assume that blood pressure readings are normally distributed with a mean of 122 and a standard deviation of6.4. If 64 people are randomly selected, find the probability that their mean blood pressure will be less than 124.
A) 0.9938
B) 0.0062
C) 0.9998
D) 0.8615

Question

Quizplus · Accepted Answer

To find the probability that the mean blood pressure of 64 randomly selected people is less than 124, we use the formula for the z-score of a sample mean: $z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $z = \frac{124 - 122}{6.4/\sqrt{64}} = \frac{2}{0.8} = 2.5$. Looking up a z-score of 2.5 in the standard normal distribution table gives a probability of approximately 0.9938, indicating the probability that their mean blood pressure will be less than 124.

Assume That Blood Pressure Readings Are Normally Distributed with a Mean