The following are the scores that 12 students obtainedon the midterm and final examinations in a course instatistics:Midterm examination Final examinationx y71 8349 6280 7673 7793 8985 7458 4882 7864 7632 5187 7380 89 (a) Find the equation of the least squares line that willenable us to predict a student’s final examination score inthis course on the basis of his or her score on the midtermexamination.(b) Predict the final examination score of a student whoreceived an 84 on the midterm examination.
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.
The following are the scores that 12 students obtained
on the midterm and final examinations in a course in
statistics:
Midterm examination Final examination
x y
71 83
49 62
80 76
73 77
93 89
85 74
58 48
82 78
64 76
32 51
87 73
80 89
(a) Find the equation of the least squares line that will
enable us to predict a student’s final examination score in
this course on the basis of his or her score on the midterm
examination.(b) Predict the final examination score of a student who
received an 84 on the midterm examination.
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