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 2019 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 2019 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?

1. (3 points) In which question (Question A or Question B) would you need to use the central limit theorem to solve? Why?

2. (4 points) For each Question A and Question 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.

Answer 1

A:

B:

In which question B) you would need to use the central limit theorem to solve because we need to use sampling distribution of sample mean.