quiz assignment of 150 questions, each question with 5 possible answers, was given to a student of which only 1 answer is correct. The student knows answers of 80 questions. What is the approximate probability that a student with no knowledge of the remaining questions, yields between 20 to 23 correct answers from his sheer guess work?
b)Assume 50 more questions are added in the assignment. How would the answer to part (i) be affected, if the student knew the answers to all the additional questions.
Answers
Given : 150 questions, each question with 5 possible answers, was given to a student of which only 1 answer is correct.
The student knows answers of 80 questions.
To Find : What is the approximate probability that a student with no knowledge of the remaining questions, yields between 20 to 23 correct answers from his sheer guess work
Solution:
Total Question = 150
Students Knows = 80
remaining Questions = 70
5 possible answers
p = probability of correct = 1/5
q = probability of incorrect = 1 - 1/5 = 4/5
Mean = nP = 70(1/5) = 14
Variance = npq = 70(1/5)(4/5) = 56/5
Standard deviation = 3.347
20 to 23 Score
Z for 20 = (20 - 14)/3.347 = 1.793 = 0.9548 %
Z for 23 = (23 - 14)/3.347 = 2.689 = 0.9964 %
probability that a student with no knowledge of the remaining questions, yields between 20 to 23 correct answers from his sheer guess work
= 0.0416
0.0416 is the required probability
Additional Questions are all known to student hence no impact
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