Math Problem Statement
Assume that women's weights are normally distributed with a mean given by 143 lb and a standard deviation given by 29 lb. (a) If 1 woman is randomly selected, find the probabity that her weight is between 108 lb and 179 lb
(b) If 6 women are randomly selected, find the probability that they have a mean weight between 108 lb and 179 lb
(c) If 95 women are randomly selected, find the probability that they have a mean weight between 108lb and 179 lb
Solution
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Math Problem Analysis
Mathematical Concepts
Normal Distribution
Z-Scores
Probability
Sampling Distribution
Formulas
Z = (X - μ) / σ
σₓ̄ = σ / √n
P(Z < z)
Theorems
Central Limit Theorem
Suitable Grade Level
Grades 11-12 or Introductory College Level
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