Fuel economy estimates for automobiles built in a certain year predicted a mean of 25.8 mpg and a standard deviation of 6.2 mpg for highway driving. Assume that a normal distribution can be applied, Within what range are 68% of the automobiles? The range for 68% of the automobiles is to mpg.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Using the 68-95-99.7 rule (or empirical rule ), we know that 68% of the automobiles are between μ-σ and μ+σ .
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