(1) (a) Suppose that you take an exam with the 400 possible points, and you are
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Question
(1) (a) Suppose that you take an exam with the 400 possible points, and you are told that the mean score is 280. You are also told that you got 350. Did you do well on the exam? Explain your answer. Correctness of your answer depends on your explanation. Reading part (b) below might help answer this question.
(b) Suppose that you take an exam with the 400 possible points, and you are told that the mean score is 280 and the standard deviation is 20. You are also told that you got 350. Did you do well on the exam? Explain your answer.
(2) Some high schools do not provide student ranks to college admissions offices. They provide only the GPAs. But, some high schools provide the GPAs with the class average while some others provide the GPAs with the class average and the standard deviation of the GPAs. Does it make a difference to college admissions offices? If so, why? Assume that GPAs are normally distributed.
(1) (a) Suppose that you take an exam with the 400 possible points, and you are told that the mean score is 280. You are also told that you got 350. Did you do well on the exam? Explain your answer. Correctness of your answer depends on your explanation. Reading part (b) below might help answer this question.
(b) Suppose that you take an exam with the 400 possible points, and you are told that the mean score is 280 and the standard deviation is 20. You are also told that you got 350. Did you do well on the exam? Explain your answer.
(2) Some high schools do not provide student ranks to college admissions offices. They provide only the GPAs. But, some high schools provide the GPAs with the class average while some others provide the GPAs with the class average and the standard deviation of the GPAs. Does it make a difference to college admissions offices? If so, why? Assume that GPAs are normally distributed.
Explanation / Answer
1.> X be a random variable denoting the score of a student in the exam.
X~Normal(280,20)
Now,P(X>350)=0.000233 that is very small.
So,the person who scored 350 have got a very good score in the exam.
2.> from the GPA,it is not possible to get a idea how a student scored w.r.t to the class performance.
with the help of class average also,we can only say whether he belongs above the average or below the average but failed to get an idea about his score w.r.t the class.
with the help of class average and standard deviation,we are able to reflect the original picture about the student's score w.r.t the class as done in question 1.
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