student of the ninth grade with a total s, scored 75 in an exam in which the m E all students was 70 and standard dev cores was 2. Bob, a student of the tent ith a total of 50 students, scored 72 in

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John, a student of the ninth grade with a total of 50
students, scored 75 in an exam in which the mean
score of all students was 70 and standard deviation
of the scores was 2. Bob, a student of the tenth
grade with a total of 50 students, scored 72 in an
exam in which the mean score of all students was 65
and standard deviation of the scores was 3. Which
of the following statements must be correct?
I.
II.
III.
(A)
(B)
(C)
(D)
(E)
John ranks higher in his class than Bob does
in his class.
There was at least one student who scored
more than John.
There was at least one student who scored
less than Bob.
Only I
Only II
Only III
Only I and III
Only II and III
Transcribed Image Text:John, a student of the ninth grade with a total of 50 students, scored 75 in an exam in which the mean score of all students was 70 and standard deviation of the scores was 2. Bob, a student of the tenth grade with a total of 50 students, scored 72 in an exam in which the mean score of all students was 65 and standard deviation of the scores was 3. Which of the following statements must be correct? I. II. III. (A) (B) (C) (D) (E) John ranks higher in his class than Bob does in his class. There was at least one student who scored more than John. There was at least one student who scored less than Bob. Only I Only II Only III Only I and III Only II and III
Expert Solution
Step 1

Given:

John

Raw score (x1) = 75

Population meanμ1=70Population standard deviation σ1=2Sample size n1=50

Bob

Raw score (x2) = 72

Population meanμ2=65Population standard deviation σ2=3Sample size n2=50

 

 

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