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

We are given that the population follows a normal distribution with a mean of 114.8 and a standard deviation of 13.1. Since we are interested in the mean of a sample of size 23, we can use the central limit theorem to conclude that the sampling distribution of the sample mean will also be approximately normal with a mean of 114.8 and a standard deviation of 13.1/sqrt(23) = 2.744.

We want to find the probability that the mean systolic blood pressure of the sample is between 119 and 122. We can standardize the sample mean using the formula:
z = (x̄ - μ) / (σ / sqrt(n))
where x̄ is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values given, we get:
z = (119 - 114.8) / (13.1 / sqrt(23)) ≈ 1.86
z = (122 - 114.8) / (13.1 / sqrt(23)) ≈ 3.03

Using a standard normal distribution table or calculator, we can find the area to the left of each z-score and subtract to get the probability in between. 
P(1.86 < z < 3.03) = P(z < 3.03) - P(z < 1.86) ≈ 0.0577

Therefore, the probability that the mean systolic blood pressure is between 119 and 122 is approximately 0.0577. Hence, the best choice is B.

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