The mean finish time for a yearly amateur auto race was 187.36 minutes with a standard deviation of 0.388 minute. The winning car, driven by Josh, finished in 186.46 minutes. The previous year's race had a mean finishing time of 112.1 with a standard deviation of 0.102 minute. The winning car that year, driven by Kate, finished in 111.89 minutes. Find their respective 2-scores. Who had the more convincing victory? Josh had a finish time with a z-score of Kate had a finish time with a z-score of (Round to two decimal places as needed.)
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.
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