You are given 9 stones which look and feel identical. One of them contains a valuable gem worth $250,000 and is actually slightly heavier than the other 8(but not enough to detect by lifting by hand) if you identify the gemstone it is yours to keep. You have a balance scale which you can use exactly 2 times. Once you have used the scale twice you never get another opportunity. How can you be certain to find the stone that contains the gem? If you guess at any point you lose your chance to win the gemstone.
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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