A student submits 7 assignments graded on the 0-100 scale. We assume that each assignment is an independent sample of his/her knowledge of the material and all scores are sampled from the same distribution. Let X₁,..., X7 denote the scores and 2 = 1 X; their average. Let p denote the unknown expected score, so that E [X₂] = p for all i. What is the maximal value z, such that the probability of observing Z≤z when p = 50 is at most 8 = 0.05?
A student submits 7 assignments graded on the 0-100 scale. We assume that each assignment is an independent sample of his/her knowledge of the material and all scores are sampled from the same distribution. Let X₁,..., X7 denote the scores and 2 = 1 X; their average. Let p denote the unknown expected score, so that E [X₂] = p for all i. What is the maximal value z, such that the probability of observing Z≤z when p = 50 is at most 8 = 0.05?
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 31CR
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Use Hoeffding's Inequality to answer the question
![A student submits 7 assignments graded on the 0-100 scale. We assume that each
assignment is an independent sample of his/her knowledge of the material and all
scores are sampled from the same distribution. Let X₁,..., X7 denote the scores
and 2 = 1 X₂ their average. Let p denote the unknown expected score, so
that E [X₂] =p for all i. What is the maximal value z, such that the probability
of observing Z≤z when p = 50 is at most = 0.05?
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa129c13b-d311-49f8-ab05-a54551674961%2F8737af98-a4c1-4680-8e08-1ab44e7d2bb6%2Fk00l3v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A student submits 7 assignments graded on the 0-100 scale. We assume that each
assignment is an independent sample of his/her knowledge of the material and all
scores are sampled from the same distribution. Let X₁,..., X7 denote the scores
and 2 = 1 X₂ their average. Let p denote the unknown expected score, so
that E [X₂] =p for all i. What is the maximal value z, such that the probability
of observing Z≤z when p = 50 is at most = 0.05?
=
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