Question

Based on years of experience, an economics professor knows that on the first principles of economics exam of the semester 13% of students will receive an A, 22% will receive a B, 35% will receive a C, 20% will receive a D, and the remainder will earn an F. Assume a 4 point grading scale (A = 4, B = 3, C = 2, D = 1, and F = 0). Define the random variable GRADE = 4, 3, 2, 1, 0 to be the grade of a randomly chosen student. a. What is the probability distribution f(GRADE) for this random variable? b. What is the expected value of GRADE? What is the variance of GRADE? Show your work. c. The professor has 300 students in each class. Suppose that the grade of the ith student is GRADEi and that the probability distribution of grades f(GRADEi) is the same for all students. Define CLASS_AVG = ?i=1 to 300 GRADEi/300. Find the expected value and variance of CLASS_AVG. d. The professor has estimated that the number of economics majors coming from the class is related to the grade on the first exam. He believes the relationship to be MAJORS = 50 + 10CLASS_AVG. Find the expected value and variance of MAJORS. Show your work.

          Based on years of experience, an economics professor knows that on the first principles of economics exam of the semester 13% of students will receive an A, 22% will receive a B, 35% will receive a C, 20% will receive a D, and the remainder will earn an F. Assume a 4 point grading scale (A = 4, B = 3, C = 2, D = 1, and F = 0). Define the random variable GRADE = 4, 3, 2, 1, 0 to be the grade of a randomly chosen student.
a. What is the probability distribution f(GRADE) for this random variable?
b. What is the expected value of GRADE? What is the variance of GRADE? Show your work.
c. The professor has 300 students in each class. Suppose that the grade of the ith student is GRADEi and that the probability distribution of grades f(GRADEi) is the same for all students. Define CLASS_AVG = ?i=1 to 300 GRADEi/300. Find the expected value and variance of CLASS_AVG.
d. The professor has estimated that the number of economics majors coming from the class is related to the grade on the first exam. He believes the relationship to be MAJORS = 50 + 10CLASS_AVG. Find the expected value and variance of MAJORS. Show your work.

Show more…

Based on years of experience, an economics professor knows that on the first principles of economics exam of the semester 13% of students will receive an A, 22% will receive a B, 35% will receive a C, 20% will receive a D, and the remainder will earn an F. Assume a 4 point grading scale (A = 4, B = 3, C = 2, D = 1, and F = 0). Define the random variable GRADE = 4, 3, 2, 1, 0 to be the grade of a randomly chosen student.
a. What is the probability distribution f(GRADE) for this random variable?
b. What is the expected value of GRADE? What is the variance of GRADE? Show your work.
c. The professor has 300 students in each class. Suppose that the grade of the ith student is GRADEi and that the probability distribution of grades f(GRADEi) is the same for all students. Define CLASSAVG = ?i=1 to 300 GRADEi/300. Find the expected value and variance of CLASSAVG.
d. The professor has estimated that the number of economics majors coming from the class is related to the grade on the first exam. He believes the relationship to be MAJORS = 50 + 10CLASSAVG. Find the expected value and variance of MAJORS. Show your work.

Added by Ver-Nica V.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Shaiju T

07/06/2022

Step 1

- \( P(\text{GRADE} = 4) = 0.13 \) - \( P(\text{GRADE} = 3) = 0.22 \) - \( P(\text{GRADE} = 2) = 0.35 \) - \( P(\text{GRADE} = 1) = 0.20 \) - \( P(\text{GRADE} = 0) = 1 - (0.13 + 0.22 + 0.35 + 0.20) = 0.10 \) Show more…

Show all steps

lock

Thanks for your feedback!

Based on years of experience, an economics professor knows that on the first principles of economics exam of the semester, 13% of students will receive an A, 22% will receive a B, 35% will receive a C, 20% will receive a D, and the remainder will earn an F. Assume a 4-point grading scale (A = 4, B = 3, C = 2, D = 1, and F = 0). Define the random variable GRADE to be the grade of a randomly chosen student, with possible values of 4, 3, 2, 1, and 0. a: What is the probability distribution f(GRADE) for this random variable? b: What is the expected value of GRADE? What is the variance of GRADE? Show your work. The professor has 300 students in each class. Suppose that the grade of the ith student is GRADEi, and that the probability distribution of grades f(GRADEi) is the same for all students. Define CLASS_AVG = ΣGRADEi/300. Find the expected value and variance of CLASS_AVG. The professor has estimated that the number of economics majors coming from the class is related to the grade on the first exam. He believes the relationship to be MAJORS = 50 + 10*CLASS_AVG. Find the expected value and variance of MAJORS. Show your work.

Play audio

Feedback

Powered by NumerAI

Shaiju T and 91 other subject Intro Stats / AP Statistics educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Recommended Videos

Recommended Textbooks

Transcript

00:01 Hello everyone, so this is the question that we have.

00:05 Now 13 % of the students will receive an a.

00:14 32 % will receive b.

00:20 35 % will receive c and 20 % will receive d.

00:31 Now we have a four grading system that a is equal to 4.

00:37 B is equal to three, c is equal to two and d is equal to one and f is equal to zero.

00:47 Remainter will receive f so for part a we need to find the probability distribution for f grade which is a random variable part b we need to give the value of grade and the variance of grade part c we need to give that if the professor has 300 students in each class so we need to give the probability distribution of grades and part d is that he has estimated and he believes in a relationship which is majors is equal to 15 plus 10 class underscore eb a bg which is average we need to be expected value so now expected value and variance of meters now let's jump on to the solution of the question if these are the given constraints so we have all the given probability we convert it into decimal so i would say part we probability of grade equal to fourth is going to be probability of a which is 0 .13 then probability of grade when it is equal to 3 is equal to the probability of b which is 0 .22 then probability of grade equal to two which is probability of grade c which is equal to 0 .35 then probability of grade equal to 1 which is probability of d which is equal to 0 .2 and then probability of grade equal to 0 which is probability of f which is equal to 0 .1 so this is going to be the probability of grade f now coming on to part p expected value so it will be given by e or say grade it is going to be 4 it is grade 4 multiplied by the decimal volume 0 .13 similarly 3 multiplied by 0 .22 this 2 multiplied by 0 .35 plus 1 multiplied by 0 .2 plus 0 multiplied by 0 .1 which is equal to 2 .08 so this is the expected grade or the expected value of rate now if we have to give the variance so e of grade square is going to be 4 square multiplied by 0 .13 plus 3 square multiplied by 0 .22 plus 2 squared multiplied by 0 .35 plus 2 squared multiplied by 0 .35 plus 1 square multiplied by 0 .2 plus 0 square multiplied by 0 .1.

04:23 That is going to be equal to 5 .66.

04:28 Now if i have to give the variance, so where of grade is going to be equal to e of grade square minus the e of grade whole square...

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later