Math Problem Statement

Suppose you buy a new car whose advertised mileage is 21 miles per gallon​ (mpg). After driving your car for several​ months, you find that its mileage is 17.1 mpg. You telephone the manufacturer and learn that the standard deviation of gas mileages for all cars of the model you bought is 1.05 mpg. a. Find the​ z-score for the gas mileage of your​ car, assuming the advertised claim is correct. b. Does it appear that your car is getting unusually low gas​ mileage?

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Z-Score
Normal Distribution

Formulas

Z-score formula: Z = (X - μ) / σ

Theorems

68-95-99.7 rule in Normal Distribution

Suitable Grade Level

Grades 10-12