PS5s - SOLUTIONS TO ISMT111 PROBLEM SET #5 (1) Answer: μ =...

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Unformatted text preview: SOLUTIONS TO ISMT111 PROBLEM SET #5 (1) Answer: μ = 8856 hours , σ = 4650 hours . X is service life in hours . X ∼ N ( μ, σ 2 ); (i) P ( X > 2160) = P Z > 2160- μ σ = P ( Z > z 1 ) = . 9251 = . 4251 + . 5 From z table , z 1 =- 1 . 44 = 2160- μ σ- 1 . 44 σ = 2160- μ ( a ) (ii) P ( X > 17040) = P Z > 17040- μ σ = P ( Z > z 2 ) = . 0392 = . 5- . 4608 From z table , z 2 = 1 . 76 = 17040- μ σ 1 . 76 σ = 17040- μ ( b ) Now, solve the two equations for the two unknowns μ and σ :- 1 . 44 σ = 2160- μ ( a ) 1 . 76 σ = 17040- μ ( b ) ( b )- ( a ) : (1 . 76 + 1 . 44) σ = 17040- 2160 , σ = 4650 Substitute σ = 4650 into either (a) (or (b)): μ = 2160 + (1 . 44)(4650) = 8856. (2) Answer: 567 . 5- 432 . 5 = 135 Sketch a normal curve for X with mean μ = 500. Let x 1 be the 25th percentile, located to the left of μ . Let x 2 be the 75th percentile, located to the right of μ ....
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PS5s - SOLUTIONS TO ISMT111 PROBLEM SET #5 (1) Answer: μ =...

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