Math Problem Statement

averages 129.08 seconds per 2.5 mile lap (in a 7 lap race) with a standard deviation of 2.26 seconds. The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps. (Source: log book of Terri Vogel) Let X be the number of seconds for a randomly selected lap. Round all answers to 4 decimal places where possible. c. The fastest 3% of laps are under ____ seconds.

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Normal Distribution
Z-scores

Formulas

Z = (X - μ) / σ
Z-table to find probabilities

Theorems

Empirical Rule of Normal Distribution
Properties of Z-scores

Suitable Grade Level

College Level (Introductory Statistics)