Math Problem Statement
Samples are drawn from a population with mean 112 and standard deviation 47. Each sample has 399 randomly and independently chosen elements. Use the Central Limit Theorem to estimate the probability that a sample mean is between 111 and 119. Write your answer as a decimal rounded to the nearest thousandth.
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Central Limit Theorem
Normal Distribution
Z-scores
Probability
Formulas
Standard Error: σ_x̄ = σ / √n
Z-score: z = (x - μ) / σ_x̄
Probability: P(z1 ≤ Z ≤ z2) = P(z2) - P(z1)
Theorems
Central Limit Theorem
Suitable Grade Level
Undergraduate (College-level Statistics)
Related Recommendation
Central Limit Theorem Probability: Sample Mean Between 111 and 119
Central Limit Theorem: Estimating Probability for Sample Mean Between 135 and 139
Calculating Probability Using the Central Limit Theorem: Sample Mean and Z-scores
Calculate Probability Using Central Limit Theorem for Sports Activity at Camford University
Find the Probability that the Mean of a Sample of 25 People is Less than 10