With a height of 69in, Marvin was the shortest president of a particular club in the past century. The club presidents of the past century have a mean height of 74.8in and a standard deviation of 1.4in. a. What is the postive difference between Marvin's height and the mean? b. How many standard deviations is that (the difference found in part a)? c. Convert Marvin's height to a z-score d. If we consider "usual" heights to be those that convert to z-scores between -2 and 2, is Marvin's height usual or unusual?
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.
With a height of 69in, Marvin was the shortest president of a particular club in the past century. The club presidents of the past century have a mean height of 74.8in and a standard deviation of 1.4in.
a. What is the postive difference between Marvin's height and the mean?
b. How many standard deviations is that (the difference found in part a)?
c. Convert Marvin's height to a z-score
d. If we consider "usual" heights to be those that convert to z-scores between -2 and 2, is Marvin's height usual or unusual?
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