Math Problem Statement
A simple random sample of size nequals43 is obtained from a population with muequals67 and sigma equals 15. (a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample mean? Assuming that this condition is true, describe the sampling distribution of x overbar. (b) Assuming the normal model can be used, determine P(x overbarless than70.6). (c) Assuming the normal model can be used, determine P(x overbar greater than or equals68.1).
Solution
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Math Problem Analysis
Mathematical Concepts
Statistics
Sampling Distribution
Central Limit Theorem
Normal Distribution
Z-scores
Formulas
Standard Error: σ_x̄ = σ / √n
Z-score: z = (x̄ - μ) / σ_x̄
Theorems
Central Limit Theorem
Suitable Grade Level
College/University-Level Statistics
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