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quizexe7 - STAT 427 Quiz/Class Exercise 7 Name With...

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STAT 427 Quiz/Class Exercise 7: Name: With Solution. 1. Suppose that X N ( - 7 , 14), find (a) P ( - 5 X 2). (b) The value of x for which P ( X x ) = 0 . 75. Note that μ = - 7 , σ = 14 . (a) P ( - 5 X 2) = P - 5 - ( - 7) 14 X - μ σ 2 - ( - 7) 14 = P ( . 53 Z 2 . 40) = Φ(2 . 40) - Φ(0 . 53) = . 9918 - . 7019 = . 2899 (b) Step 1. Find the 75th percentile of Z first, which is z = . 67. (That is, P ( Z z ) = . 75.) Step 2. Transform back, the x = μ + σz = - 7 + 14 × . 67 = - 4 . 49. 2. Calculate the probability using a normal approximation:
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