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Home Q & A Board Science-Related Homework Help Mathematics Statistics and Probability
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liljay liljay
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4 years ago
Basketball player heights Assume the heights of high school basketball players are normally distributed. For boys the mean is 74 inches with a standard deviation of 4.5 inches, while girl players have a mean height of 70 inches and standard deviation 3 inches. At a mixed 2-on-2 tournament teams are formed by randomly pairing boys with girls as teammates.

a. On average, how much taller do you expect the boy to be?
b. What will be the standard deviation of the difference in teammates' heights?
c. On what fraction of the teams would you expect the girl to be taller than the boy?
Textbook 
Stats: Modeling the World

Stats: Modeling the World


Edition: 4th
Authors:
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#1
4 years ago
a. E(B - G) = E(B) - E(G) = 74 - 70 = 4 inches
b. Var(B - G) = Var(B) + Var(G) = (4.5)2 + (3)2 = 29.25. SD(X) = = 5.4
c. Let D = difference between boy's height minus girl's height
P(D < 0) = P = P(z < -0.7407) = 0.2294
So, about 22.94% of the time you could expect the girl to be taller than the boy.
liljay Author
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#2
4 years ago
I appreciate what you did here, answered it correctly Smiling Face with Open Mouth
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