Empirical Rule
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.
Abdomen data:
83.0, 87.9, 85.2, 88.6, 77.1, 85.3, 100.0, 94.4, 81.9, 88.5, 82.5, 100.5, 76.5, 86.4, 90.7, 83.6, 106.8, 77.6, 102.9, 90.9, 79.7, 73.9, 79.1, 72.8, 88.2, 100.1, 89.6, 95.9, 98.8, 76.3, 83.5 105.0, 90.8, 83.5, 84.5 101.8, 76.6, 76.4, 88.7, 92.4, 81.2, 91.6, 97.5, 80.0, 88.7, 100.5, 95.6, 92.1, 96.4, 74.6, 83.4, 106.0, 96.4, 92.8, 95.1, 90.4, 100.4, 115.9, 90.8, 81.9, 75.0, 90.3, 90.3, 108.8, 79.4, 83.2, 110.3, 91.6, 92.7, 76.0, 79.5, 86.1, 104.5, 104.6
Assume that the abdomen circumference of males have a distribution that is
approximately bell-shaped. Using the mean (= 89.7) and standard deviation (=9.9) as estimates of the population mean and standard deviation,
a. Construct a diagram, using the Empirical Rule, to illustrate the percentages
of data values in each of the 8 sections that diagram includes.
b. Between what two measurements will about 95% of the abdomen
circumferences fall?
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