The mean number of miles driven per vehicle annually in the...

The mean number of miles driven per vehicle annually in the United States is 12,494 miles. Choose a randomly selected vehicle, and assume the annual mileage is normally distributed with a standard deviation of 1290 miles. What is the probability that the vehicle was driven more than 15,000 miles? Less than 8000 miles? Would you buy a vehicle if you had been told that it had been driven less than 6000 miles in the past year?

Key Concepts

Normal Distribution

The normal distribution is a fundamental probability distribution in statistics, characterized by its symmetric, bell-shaped curve. It is used to model many natural phenomena where values tend to cluster around a mean, with the probability of extreme values decreasing as they move further from the mean.

Standard Deviation

Standard deviation measures the dispersion or spread of a set of data points relative to the mean. In the context of a normal distribution, it helps determine how concentrated the data is around the mean and is key to calculating probabilities for different intervals.

Z-Score

A z-score is a standardized metric that quantifies the number of standard deviations a data point is from the mean. It allows for the conversion of a raw score into a common scale, making it possible to calculate probabilities using the standard normal distribution.

Probability Calculations

Probability calculations in the context of a normal distribution involve using the z-score to determine the likelihood that a data point falls within a given range. This process typically includes converting raw scores to z-scores and consulting standard normal distribution tables or using statistical software.

Decision Making Based on Statistical Analysis

This concept emphasizes the use of statistical evidence to inform decisions. By understanding and calculating probabilities, one can assess the likelihood of certain outcomes and make informed choices, such as evaluating the condition or reliability of a product based on its statistical performance.

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