Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information. 73 73 67 42 64 39 75 48 86 51 44 51 Ex = 438, Ey = 275, Ex² = 32264, Ey² = 12727, Exy = 20231, and r= 0.827. (d) Find the predicted percentage ŷ of successful field goals for a player with x = 79% successful free throws. (Round your answer to two decimal places.) % (e) Find a 90% confidence interval for y when x = 79. (Round your answers to one decimal place.) lower limit upper limit %

Question
Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of
successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.
73
73
67
42
64
39
75
48
86
51
44
51
Ex = 438, Ey = 275, Ex² = 32264, Ey² = 12727, Exy = 20231, and r= 0.827.
(d) Find the predicted percentage ŷ of successful field goals for a player with x = 79% successful free throws. (Round your answer to two decimal places.)
%
(e) Find a 90% confidence interval for y when x = 79. (Round your answers to one decimal place.)
lower limit
upper limit
%
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Transcribed Image Text

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information. 73 73 67 42 64 39 75 48 86 51 44 51 Ex = 438, Ey = 275, Ex² = 32264, Ey² = 12727, Exy = 20231, and r= 0.827. (d) Find the predicted percentage ŷ of successful field goals for a player with x = 79% successful free throws. (Round your answer to two decimal places.) % (e) Find a 90% confidence interval for y when x = 79. (Round your answers to one decimal place.) lower limit upper limit %

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