The heights of women aged 20– 29 in the United States are approximately Normal with mean 64.2 inches and standard deviation 2.8 inches. The heights of men aged 20– 29 in the United States are approximately Normal with mean 69.4 inches and standard deviation 3.0 inches. What is the ?z‑score for a woman 5.5 feet tall? (Enter your answer rounded to two decimal places.) ?= What is the z‑score for a man 5.5 feet tall? (Enter your answer rounded to two decimal places.) ?=z= What information do the z‑scores give that the original non‑standardized heights do not? The z‑scores show us that the woman is slightly taller than average, while the man is much shorter than average. The z‑scores do not give us any additional information, since we already know that the man and woman have equal heights. The z‑scores show us that the woman is slightly shorter than average, while the man is much taller than average. The z‑scores show that the woman is slightly different from the average, while the man is very different from the average.
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.
The heights of women aged 20– 29 in the United States are approximately Normal with mean 64.2 inches and standard deviation 2.8 inches. The heights of men aged 20– 29 in the United States are approximately Normal with mean 69.4 inches and standard deviation 3.0 inches.
What is the ?z‑score for a woman 5.5 feet tall? (Enter your answer rounded to two decimal places.)
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