A question has 40 multiple choice questions. Each question has four answer optio
ID: 2927426 • Letter: A
Question
A question has 40 multiple choice questions. Each question has four answer options (A, B, C, and D).
A. Assuming that the students have been coming to class and have some related knowledge, do scores on this test represent a binomial random variable? Why or why not?
B. Assuming that the students have no prior knowledge and randomly guess on all questions, do scores on this test represent a binomial random variable? Why or why not?
C. Assuming that all students randomly guess on all questions, compute the expected mean and standard deviation of the distribution of quiz scores. Be sure to use equation editor here.
D. Assuming that a student is randomly guessing on all questions, what is the probability that he or she will get 24 or more questions correct? (NOTE: This would be the probability of scoring a 60% or better on a traditional grading scale this would be barely passing)
E. Assuming that all students randomly guess on all questions, what scores will separate the middle 95% from the outer 5%?
Explanation / Answer
Answer:
A question has 40 multiple choice questions. Each question has four answer options (A, B, C, and D).
A. Assuming that the students have been coming to class and have some related knowledge, do scores on this test represent a binomial random variable? Why or why not?
Not a binomial random variable because the probability of choose the correct is not same for all questions.
B. Assuming that the students have no prior knowledge and randomly guess on all questions, do scores on this test represent a binomial random variable? Why or why not?
This is a binomial random variable because the probability of choose the correct is same for all questions.
C. Assuming that all students randomly guess on all questions, compute the expected mean and standard deviation of the distribution of quiz scores. Be sure to use equation editor here.
n=40, p=0.25
Expectation = np = 10
Variance = np(1 - p) = 7.5
Standard deviation = 2.7386
D. Assuming that a student is randomly guessing on all questions, what is the probability that he or she will get 24 or more questions correct? (NOTE: This would be the probability of scoring a 60% or better on a traditional grading scale this would be barely passing)
Z value for 24, z =(24-10)/2.7386 = 5.11
P( x 24) = P( z >5.11)
=0.0000
E. Assuming that all students randomly guess on all questions, what scores will separate the middle 95% from the outer 5%?
Mean ± 2 standard deviations separate the middle 95% from the outer 5%.
Lower limit = 10-2*2.7386 = 4.5228
Upper limit = 10+2*2.7386 15.4772