Math Problem Statement

1.1 A bottling company uses a filling machine to fill plastic bottles with a popular cola. The bottles are supposed to contain 300 ml. In fact, the contents vary according to a normal distribution with mean of 298 ml and standard deviation of 3 ml. 1.1.1. What is the probability that an individual bottle contains more than 295 ml? [5] 1.1.2 What is the probability that the mean contents of the bottles in a six-pack is between 295 ml and 299 ml? [6]

Solution

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Math Problem Analysis

Mathematical Concepts

Normal Distribution
Z-score
Standard Deviation

Formulas

Z-score formula: Z = (X - μ) / σ
Standard deviation of the mean: σ_mean = σ / √n

Theorems

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Suitable Grade Level

University Level