Math Problem Statement

When women were finally allowed to become pilots of fighter​ jets, engineers needed to redesign the ejection seats because they had been originally designed for men only. The ejection seats were designed for men weighing between 140 lb and 201 lb. Weights of women are now normally distributed with a mean of 175 lb and a standard deviation of 48 lb. Complete parts​ (a) through​ (c) below. Question content area bottom Part 1 a. If 1 woman is randomly​ selected, find the probability that her weight is between 140 lb and 201 lb. The probability is approximately select: 0.4733 0.4733. ​(Round to four decimal places as​ needed.) Part 2 b. If 28 different women are randomly​ selected, find the probability that their mean weight is between 140 lb and 201 lb. The probability is approximately

enter your response here. ​(Round to four decimal places as​ needed.)

Solution

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Math Problem Analysis

Mathematical Concepts

Normal Distribution
Z-scores
Probability
Central Limit Theorem

Formulas

Z = (x - μ) / σ
Standard error = σ / √n
P(a ≤ X ≤ b) = P(Z1 ≤ Z ≤ Z2)

Theorems

Central Limit Theorem

Suitable Grade Level

College-level Statistics