2. Two classes took an exam. In the first class, the average score was exactly 78%. In the second class, the average score was exactly 86%. But when the two classes were treated as one large group, the average was not 82%. a. How is this possible? b. What's the highest that the combined average could be? What's the lowest? c. Under what circumstances would the average of the two class averages be the same as the average you get when you treat the two classes as one large group? Explain your answer and be as complete as you can. Be sure to justify your answers.
2. Two classes took an exam. In the first class, the average score was exactly 78%. In the second class, the average score was exactly 86%. But when the two classes were treated as one large group, the average was not 82%. a. How is this possible? b. What's the highest that the combined average could be? What's the lowest? c. Under what circumstances would the average of the two class averages be the same as the average you get when you treat the two classes as one large group? Explain your answer and be as complete as you can. Be sure to justify your answers.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Can you please answer number 2, all parts: thank you!!
Transcribed Image Text:2. Two classes took an exam. In the first class, the average score was exactly 78%.
In the second class, the average score was exactly 86%. But when the two
classes were treated as one large group, the average was not 82%.
a. How is this possible?
b. What's the highest that the combined average could be? What's the lowest?
c. Under what circumstances would the average of the two class averages be
the same as the average you get when you treat the two classes as one
large group? Explain your answer and be as complete as you can.
Be sure to justify your answers.
3. Garrison Keillor describes Lake Wobegon as a place where "the children are all
above average."
Suppose someone measured all 85 ten-year-olds in the town and found that
their average height was 4 feet 7 inches.
a. Is it possible that all the ten-year-olds are taller than 4 feet 7 inches?
b. If not, what is the largest number of ten-year-olds who could be taller than
that? Explain your answer.
c. Is it possible that Garrison Keillor is right, and all the ten-year-olds in
Lake Wobegon are taller than average? What could that mean?
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