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

Question

Quizplus · Accepted Answer

To find the probability that the mean systolic blood pressure for a sample of 23 women aged 18-24 is between 119 and 122 mm Hg, we use the formula for the standard error of the mean: SE = σ / √n, where σ is the population standard deviation and n is the sample size. Here, σ = 13.1 and n = 23, so SE = 13.1 / √23 ≈ 2.733. We then convert the target range (119 to 122 mm Hg) into z-scores using the formula z = (X - μ) / SE, where X is the target mean blood pressure, μ is the population mean, and SE is the standard error of the mean. For X = 119, z = (119 - 114.8) / 2.733 ≈ 1.54. For X = 122, z = (122 - 114.8) / 2.733 ≈ 2.64. Using the standard normal distribution, we find the probabilities corresponding to these z-scores and subtract the smaller from the larger to find the probability of the mean blood pressure being between 119 and 122 mm Hg. The probability corresponding to z = 1.54 is approximately 0.9382, and for z = 2.64, it is approximately 0.9959. The difference gives us the probability of the mean being in the target range, which is approximately 0.0577.

For Women Aged 18-24, Systolic Blood Pressures Are Normally Distributed