Math Problem Statement

John Beale of Stanford, California, recorded the speeds of cars driving past his house, where the speed limit read 35 mph. The mean of 100 representative readings was 38.61 mph, with a standard deviation of 3.48 mph. Questions: a) How many standard deviations from the mean would a car going the speed limit be? b) Which would be more unusual, a car traveling 49 mph or one going 25 mph? c) The standard deviations for the boxes in part B are?

Solution

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Math Problem Analysis

Mathematical Concepts

Standard Deviation
Z-score
Normal Distribution

Formulas

Z = (X - μ) / σ

Theorems

Empirical Rule (68-95-99.7 rule)

Suitable Grade Level

Grade 10-12