A university gives every student an entrance exam at the beginning of their fres

Question

A university gives every student an entrance exam at the beginning of their freshman year. The exam includes general knowledge questions and specific subject questions. Scores are recorded in each students file and used for course placement purposes. Each year 25 students are randomly sampled for further questioning and testing. The scores for all students in the Fall of 2015 are normally distributed with mean 81 and standard deviation 5.

Suppose you were asked the next two questions (don’t answer them yet!):

Question A: “What is the probability a randomly chosen student from the Fall 2015 scores better than 83 on the exam?”

Question B: “What is the chance the average of the sampled 25 students on the entrance exams is more than 83?

a.      In which question (Question A or Question B) would you need to use the central limit theorem to solve? Why?

b.     For each Question A and B the solution and distribution is below.

Your tasks are to:

1.     Indicate which graph/solution represents the correct answer for each question.

2.     State why you believe the graph/solution is correct.

3.     State why you believe the remaining graphs/solutions are incorrect.

Plot A 0.977 78 79 80 81 82 83 84 Plot C 0.345 66 71 76 81 86 91 96 Plot B 0.023 78 79 80 81 82 83 84 Plot D 0.655 T T T T T 66 71 76 81 86 91 96

Explanation / Answer

(a) For Question B we need to use the central limit theorem that the average of a sample follows normal distribuition with the same mean and standard deviation = standard deviation/sqrt(n) = 5/5 =1

(b) The scale should be 5 as the standard deviation is 5.

Hence for question A Plot C is the correct option to chose since we need to check for the area above 83 and 6 is the standrad deviation in this case

For Question B Plot B is the correct option to chose since we have standard deviation = 1 (x interval length) which is correctly shown in plot B and area above 83 is required thing

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