In a certain type of metal test specimen, the normal stress on a specimen is known to be functionally related to the shear resistance. The following is a set of coded experimental data on the two varlables: Normal Stress, x (MPa) Shear Resistance, y (MPa) 26.8 26.5 25.4 27.3 28.9 24.2 23.6 27.1 27.7 23.6 23.9 25.9 24.7 26.3 28.1 22.5 26.9 21.7 27.4 21.4 22.6 25.8 25.6 24.9 (a) Determine the equation of the best-fit line that relates the normal stress and the shear resistance of the metal specimen. Evaluate the standard deviation as well. (b) Predict the magnitude of the normal stress acting on the metal specimen provided that its shear resistance is 25.0 MPa. (c) Predict the magnitude of the shear resistance of the metal specimen if a normal stress of 28.0 MPa is acting on it.
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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