Arthur has two children, Zeke and Lucy, who competed in a track meet. The results were as follows: Zeke ran the 400 m event in 55.9 seconds. The mean time for all runners was 56.6 seconds and the standard deviation was 2.07 seconds. Lucy ran the 200 m event in 26.4 seconds. The mean time for all runners was 27.8 seconds and the standard deviation was 1.81 seconds. What was the z-score for Zeke's time? What was the z-score for Lucy's time? Who ran a better race, relatively speaking? Zeke O Lucy
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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