Assuming that the heights of college women are normally distributed with mean 70 inches and standard deviation 3.5 inches, answer the following questions. (Hint: Use the figure below with mean μ and standard deviation σ.) (a) What percentage of women are taller than 70 inches? % (b) What percentage of women are shorter than 70 inches? %
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.
Assuming that the heights of college women are
%
(b) What percentage of women are shorter than 70 inches?
%
(c) What percentage of women are between 66.5 inches and 73.5 inches?
%
(d) What percentage of women are between 63.0 and 77.0 inches?
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