Q3 with a mean value of of ux = 1300 kN and a coefficient of variation of ôx = 0.20. The capacity (X) of an isolated spread footing under a column is modeled by a normal distribution a) If the column is subjected to a load of 600 kN, calculate the probability of failure of the foundation. (see the figure below) b) If the failure probability of the foundation needs to be limited to 0.03, what is the maximum load that can be applied to the column? Load = 600 kN X=Capacity (resistance)
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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