Ask questions and get helpful responses.
Ask a New Question
  1. Questions

math, probability

Exercise: CLT applicability

Consider the class average in an exam in a few different settings. In all cases, assume that we have a large class consisting of equally well prepared students. Think about the assumptions behind the central limit theorem, and choose the most appropriate response under the given description of the different settings.

1. Consider the class average in an exam of fixed difficulty.

(a) The class average is approximately normal

(b) The class average is not approximately normal because the student scores are strongly dependent

(c) The class average is not approximately normal because the student scores are not identically distributed

2. Consider the class average in an exam that is equally likely to be very easy or very hard.

(a) The class average is approximately normal

(b) The class average is not approximately normal because the student scores are strongly dependent

(c) The class average is not approximately normal because the student scores are not identically distributed

3. Consider the class average if the class if split into two equal size sections. One section gets an easy exam and the other section gets a hard exam.

(a) The class average is approximately normal

(b) The class average is not approximately normal because the student scores are strongly dependent

(c) The class average is not approximately normal because the student scores are not identically distributed

4. Consider the class average if every student is (randomly and independently) given either an easy or a hard exam.

(a) The class average is approximately normal

(b) The class average is not approximately normal because the student scores are strongly dependent

(c) The class average is not approximately normal because the student scores are not identically distributed

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
diogenes

  1. 1. (a)
    2. (b)
    3. (a)
    4. (a)

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    diogenes

  2. 1. Since students are equally well-prepared and the difficulty level is fixed, the only randomness in a student's score comes from luck or accidental mistakes of that student. It is then plausible to assume that each student's score will be an independent random variable drawn from the same distribution, and the CLT applies.

    2. Here, the score of each student depends strongly on the difficulty level of the exam, which is random but common for all students. This creates a strong dependence between the student scores, and the CLT does not apply.

    3. This is more subtle. The scores of the different students are not identically distributed. However, let π‘Œπ‘– be the score of the 𝑖 th student from the first section and let 𝑍𝑖 be the score of the 𝑖 th student in the second section. The class average is the average of the random variables (π‘Œπ‘–+𝑍𝑖)/2 . Under our assumptions, these latter random variables can be modeled as i.i.d., and the CLT applies.

    4. Unlike part (2), here the student scores are i.i.d., and the CLT applies.

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
    diogenes

Respond to this Question

First Name

Your Response

Similar Questions

  1. English

    1. I am into sports. (What is the meaning of this sentence?) 2. Exercise is good for the health. 2-1. Exercise is good for health. 2-2. Exercise is good for your health. 2-3. Exercise does good for people. (Are all correct?) 3.

  2. Statistics

    In your biology class, your final grade is based on several things: a lab score, score on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 25% of

  3. math

    In a certain class there are 12 boys and 18 girls. If the class average for an algebra exam is 90 and the boys' average score is 87, what is the girls' average score?

  4. Algebra

    A student in a Pre-Calculus class has test scores of 70, 73, 61, and 79. The final exam is worth 2 test grades. Write a linear equation that models this problem, where x is the grade on the final exam and y is the student's grade

  1. working with data

    josephs final averages in science class are shown in the table below. homework % toward final grade-20% average-93 quizzes % toward final grade-20% average-92 tests % toward final grade-40% average-85 final exam % toward final

  2. math

    In a course a student's final exam is weighted as heavily as his mid term exam.if a student receives a score of 84 on his final exam 90 on his midterm,what is the average for the course?

  3. Programming

    Write the pseudocode to represent the following: Input: Input the name, address, and exam percentage of a students. Process: Calculate the total percentage marks of all the students and the class average. Output: For each student,

  4. JAVA PROGRAMMING

    im new to java and this is my first assignment can anyone help me solving it: compile the class final grades, based on the students’ scores obtained in the classwork, mid-term, and final exams. According to the course syllabus,

  1. Statistics

    In Professor Smith's statistics course, the correlation between students' total scores before the final exam and their final exam scores is r = 0.67. The pre-exam totals for all students in the course have a mean of 275 and a

  2. Statistics

    An instructor has graded 25 exam papers submitted by students in a class of 26 students, and the average so far is 71. (The maximum possible score is 100.) A) To raise the class average by 1 point, the score on the last paper has

  3. Probability

    CLT for the binomial Let X be binomial with parameters n=49 and p=1/10. The mean of X is: unanswered The standard deviation of X is: unanswered The CLT, together with the 1/2-correction, suggests that P(X=6)β‰ˆ unanswered You may

  4. Math (Algebra 1)

    Juan’s first 3 exam scores are 85, 93, and 87. What does he need to score on his next exam to average 90 for all 4 exams? let x represent the score on his next exam (put this in a multi-step equation) PLEASE HELP

Still need help? You can ask a new question.