Math Problem Statement

The average salary of newly graduated students with bachelor’s degrees in CS&AI is $53,600, with a standard deviation of $3200. Approximate the probability that the average salary of a sample of 12 recently graduated CS&AI engineers i) Less than $50,000 ii) between $52,000 and $54,000 iii) exceeds $55,000

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Normal Distribution
Central Limit Theorem
Probability

Formulas

Standard Error of the Mean (SEM): σₓ̄ = σ / √n
Z-score for sample means: Z = (X̄ - μ) / σₓ̄

Theorems

Central Limit Theorem

Suitable Grade Level

Undergraduate