You should come up with your own response first. Only after posting yours, you m

Question

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    The final writing must be of your own based on your understanding.

Prompts: (Answer both)

(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.

a)

Well, what I know is my score is above average, but I don't have an idea what proportion of students scored lower than me.

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b)

It appears I did well, because I am (350-280)/20 = 3.5 standard deviations above the mean. Hence, very few people, if at all, scored above my score.

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2.

As we can see in part 1, knowing the standard deviation gives you a better idea of percentile ranks, because you can calculate z scores, and hence, ranks. If only the average is given, you only know whether a score is above or below the mean.

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