Solve the problem.
-For women aged 18-24, systolic blood pressures (in mm Hg)are normally distributed with a mean of 114.8 and a standard deviation of 13.1. If 23 women aged 18-24 are randomly selected, find the probability that their mean systolic blood pressure is between 119 and 122.

Question

Quizplus · Accepted Answer

To find the probability that the mean systolic blood pressure of 23 randomly selected women aged 18-24 is between 119 and 122, 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, $\sigma = 13.1$ and $n = 23$, so $\sigma_{\bar{x}} = \frac{13.1}{\sqrt{23}}$.Next, we convert the given blood pressure values to z-scores using the formula $z = \frac{\bar{x} - \mu}{\sigma_{\bar{x}}}$, where $\bar{x}$ is the sample mean and $\mu$ is the population mean. For 119 mm Hg, $z_1 = \frac{119 - 114.8}{\sigma_{\bar{x}}}$ and for 122 mm Hg, $z_2 = \frac{122 - 114.8}{\sigma_{\bar{x}}}$.Finally, we find the probabilities corresponding to these z-scores using the standard normal distribution table and subtract the smaller probability from the larger one to find the probability that the mean systolic blood pressure is between 119 and 122 mm Hg. The calculation yields a probability of 0.0577, making option B the correct answer.

Solve the Problem. -For Women Aged 18-24, Systolic Blood Pressures (In Mm Hg)are