Math Problem Statement

The diameter of a brand of tennis balls is approximately normally​ distributed, with a mean of 2.64 inches and a standard deviation of 0.05 inch. A random sample of 12 tennis balls is selected. 

The probability is 57​% that the sample mean will be between what two values symmetrically distributed around the population​ mean?  Give the lower boundary. 

(Round answer to two decimal places.)

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Normal Distribution
Sampling Distribution

Formulas

Standard Error of the Mean: SE = σ / sqrt(n)
Boundary Formula: Boundary = μ ± (z × SE)

Theorems

Empirical Rule
Central Limit Theorem

Suitable Grade Level

Grades 10-12