STA 2023 Quiz 4 Solutions.pdf - Name Panther ID Spring 2018 STA 2023 Statistics for Business Economics Quiz 4 Solutions There are 2 problems for a total

STA 2023 Quiz 4 Solutions.pdf - Name Panther ID Spring 2018...

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Name: _________________________ Panther ID: _________________________ Spring 2018 STA 2023 Statistics for Business & Economics Quiz # 4 Solutions There are 2 problems for a total of 20 points. Show your work. Please write your work neatly. Problem 1 (10 points). Let Y be a normal random variable having μ = -5 and σ 2 =9. a) Compute P(-7 < Y < -2) 𝑃(−7 < ? < −2) = 𝑃(? < −2) − 𝑃(? < −7) = 𝑃 (? < −2 − (−5) 3 ) − 𝑃 (? < −7 − (−5) 3 ) = 𝑃(? < 1) − 𝑃 (? < − 2 3 ) = 0.8413 − [1 − 0.7486] = 𝟎. ????. b) Compute P(|Y+2 |≥ 2). 𝑃(|? + 2| ≥ 2) = 𝑃(? > 0) + 𝑃(? < −4) = 𝑃 (? > 5 3 ) + 𝑃 (? < 1 3 ) = [1 − 0.9525] + 0.6293 = 𝟎. ???? c) Find y 0 so that P(Y> y 0 )=0.85. P ( ? + 5 3 > 𝑦 0 + 5 3 ) = 0.85 P (? > 𝑦 0 + 5 3 ) = 0.85 Therefore, −(𝑦 0 +5) 3 = 1.04 ; -y 0 = 3.12+5 and y 0 = -8.12 .
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Problem 2 (10 points). Suppose that the population of FIU students have an average height of 67 inches
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