Math Problem Statement

The response times of a customer service team for a particular company follow a normal distribution with a mean of 30 minutes and a standard deviation of 6 minutes. What is the probability that at least one fifth of forty randomly selected customers has to wait more than 35 minutes to receive a response? Use approximation with a normal approximation.

Solution

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Math Problem Analysis

Mathematical Concepts

Normal Distribution
Binomial Distribution
Normal Approximation to Binomial Distribution
Probability

Formulas

Z = (X - μ) / σ
P(X > 35) = 1 - P(Z < (X - μ) / σ)
μ = np
σ = √(np(1 - p))
Z = (X - μ) / σ

Theorems

Normal Approximation to Binomial Distribution
Central Limit Theorem
Continuity Correction

Suitable Grade Level

College/University Level