Provide an appropriate response.
-Assume that blood pressure readings are normally distributed with a mean of 122 and a standard deviation of 9.6. If 144 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 144 randomly selected people is less than 124, we use the formula for the standard error of the mean: $\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the population standard deviation and $n$ is the sample size. Here, $\sigma = 9.6$ and $n = 144$, so $\sigma_{\bar{x}} = \frac{9.6}{\sqrt{144}} = \frac{9.6}{12} = 0.8$. We then calculate the z-score for a mean of 124: $z = \frac{\bar{x} - \mu}{\sigma_{\bar{x}}} = \frac{124 - 122}{0.8} = 2.5$. Looking up the z-score of 2.5 in the standard normal distribution table gives a probability of 0.9938 that the mean blood pressure of 144 people will be less than 124.

Provide an Appropriate Response 124.124 .124. A) 0.99380.99380.9938 B) 0.00620.00620.0062 C) 0.99980.99980.9998 D) 0.86150.86150.8615

Provide an Appropriate Response $124 .$ A) $0.9938$ B) $0.0062$ C) $0.9998$ D) $0.8615$