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

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Unformatted text preview: 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 = (a) √ 14. P (−5 ≤ X ≤ 2) 2 − (−7) −5 − (−7) X −µ √ ≤√ =P ≤ σ 14 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: P (45 ≤ X ≤ 55) where X ∼ B (100, .5). Note that n = 100, p = 0.5 P (45 ≤ X ≤ 55) = P (X ≤ 55) − P (X ≤ 44) =Φ 55 + .5 − 100 × .5 100 × .5 × (1 − .5) −Φ 44 + .5 − 100 × .5 100 × .5 × (1 − .5) = Φ(1.1) − Φ(−1.1) = .8643 − .1357 = .7286 1 ...
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This note was uploaded on 04/16/2010 for the course STAT 427 taught by Professor Staff during the Spring '08 term at Ohio State.

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