Math Problem Statement

Problem # 2 (12.5 pts). For women aged 18-24, systolic blood pressure (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1 (based on data from the National Health Survey). Hypertension is commonly defined as a systolic blood pressure above 140. (Draw the bell curve).

a) If a sample of 40 women is selected in that age bracket is randomly selected, find the probability that their mean systolic blood pressure is between 139 and 140. (Draw the bell curve).

Solution

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Math Problem Analysis

Mathematical Concepts

Normal Distribution
Sampling Distribution
Standard Error of the Mean
Z-score

Formulas

Standard Error of the Mean (SEM) = σ / √n
Z-score: Z = (X - μ) / SEM

Theorems

Central Limit Theorem

Suitable Grade Level

Advanced College