30% of the soil samples obtained from a proposed construction site gave test results for compressive strength of more than 3.5 tons per square foot. The coefficient of variation of the strengths is known to be 20%. Calculate: a) the mean soil strength, b) the standard deviation of soil strengths, c) the probability of soil strengths falling between 2.7 and 4.0 tons per square foot. State any assumptions made
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.
30% of the soil samples obtained from a proposed construction site
gave test results for compressive strength of more than 3.5 tons per
square foot. The coefficient of variation of the strengths is known to
be 20%. Calculate:
a) the mean soil strength,
b) the standard deviation of soil strengths,
c) the
square foot. State any assumptions made.
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