Math Problem Statement

Suppose you have a normally distributed population with a mean of 47.76, standard deviation of 2.3. Consider the sampling distribution with sample size of 36. There is an interval (Lower, Upper) centered at 47.76 that contains 83% of the sampling distribution. Find the Upper bound of this interval.

Round your answers to 4 decimal places.

Solution

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Math Problem Analysis

Mathematical Concepts

Sampling Distribution
Normal Distribution
Z-Score
Confidence Interval

Formulas

Standard Error (SE) = σ / √n
Upper Bound = μ + z × SE

Theorems

Central Limit Theorem
Empirical Rule

Suitable Grade Level

College-Level Statistics or Advanced High School Statistics