Probability Analysis of System Components and Production Lines
School
Florida International University**We aren't endorsed by this school
Course
ESI 3215
Subject
Industrial Engineering
Date
Dec 10, 2024
Pages
1
Uploaded by BaronKnowledgeTurtle510
Assignment 2 Problems 3 1. A system consists of four components conn H i ; o e S T s ectedasshown.(lpomt)a : P (system tunttions)=(=(0 )y 0.2-0.05+0.3) : P(:yflpw Punctions) = |- (0.0003) E/wm, funttrons )= 0 w;‘l 6 Assume A, B, C, and D function independently. 0' 2 If the probabilities that A, B, C, and D fail are 0.1, 0.2, 0.05, and 0.3 respectively, what is the probability that the system functions? Two production lines are used to pack sugar into 5 kg bags. Line 1 produces twice as many bags as does line 2. One percent of bags from line 1 are defective in that they fail to meet a purity specification, while 3% of the bags from line 2 are defective. A bag is randomly chosen for inspection. ( 1 point, each part is 0.25 points) a. What is the probability that it came from line 1? b. What is the probability that is defective? c. Ifthe bag is defective, what is the probability that it came from line 1? d. If the bag is not defective, what is the probability that it came from line 1? 3. The reading given by a thermometer calibrated in ice water (actual temperature 0° C) is a random variable with probability density function (1 point, each part is 0.2 point) _ (0751 —x%) —1<x<1 )= {0 otherwise a. What is the probability that the temperature reads above 0° C? b. What is the probability that the reading is within 0.25° C of the actual temperature 0° C? c. What is the mean reading? d. What is the median reading? e. What is the standard deviation? 2)a. p{’70)’/( 0 2 (- x)ds
