2. A teacher gives a test to a class of 20 students Is it possible that 90% ofth
ID: 3318373 • Letter: 2
Question
2. A teacher gives a test to a class of 20 students Is it possible that 90% ofthe class scores above average? If so, give an example oftest scores for which this is the case. If not explain why not a. b. Is it possible that 90% of the class scores below average? If so, give an example of test scores for which this is the case. If not, explain why not A radio program describes a fictional town in which "all the children are above average." In what sense is it possible that all the children are above average? In what sense is it not possible that all the children are above average? 3.Explanation / Answer
Question 2
Part a
Yes, it is possible that 90% of the class scores above average. Suppose, two students in the class have score equals 5 or 10 out of 100 and remaining 18 students have scores equal 60 to 65. There would not be more difference in scores of 18 students. Then it will found that 90% of the class scores are above average. This is only exceptional scenario and it is not possible in practical, because we know that scores are approximately normally distributed.
Part b
Yes, it is possible that 90% of the class scores are below average. Suppose, only two students in the class are very clever and they have scores more than 95 out of 100, and remaining 18 students have scores less than 40. Then in this case, 90% of the class scores will be below average. This is an exceptional case and in general it is not possible as scores follow an approximate normal distribution.
Question 2
It is possible that all the children are above average if the radio program considers a population of more than one town or entire state. It is not possible in the sense if the radio program considers the population of only single fictional town.
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