he data set provided by JOHN shows the number of yearly values of flood damage relief items represented by y and the annual rainfall (in centimetres) represented by x over a period of 10 years. y(000s) x (cm) 4.0 110
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.
QUESTION2
The data set provided by JOHN shows the number of yearly values of flood damage relief items represented by y and the annual rainfall (in centimetres) represented by x over a period of 10 years.
y(000s) x (cm)
4.0 110
1.5 250
1.2 220
3.0 150
3.0 450
2.5 200
2.0 210
2.0 230
1.1 290
3.0 100
(a) Find the standard deviations of x and y.
(b) Find the equation of the least-squares regression line, assuming that the value of the relief items for flood damage depend on the amount of rainfall.
(c) Calculate the
(d) Use your results to predict the value of flood damage amount in years with 50cm of Rainfall, in years with 250cm of rainfall and in years with 550cm of rainfall. Comment on the likely accuracy of your predictions.
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