MATH 110 Module 4 Exam Solutions 2022 (Scored 100%)

MATH 110 Module 4 Exam Solutions 2022 (Scored 100%) A factory has eight safety systems. During an emergency, the probability of any one of the safety systems failing is .08. What is the probability that six or more safety systems will fail during an emergency? f(x) = ( (n!) / (x!(n-x)!) ) x ( (p^x) x ((1-p)^n-x)) ) n = 8 x = 6, 7, 8 (number of failures) p = 0.08 6 failures: n = 8 x = 6 p = 0.8 n-x = 8-6 = 2 ( (8!) / (6!(2)!) ) x ( (0.08^6) x ((1-0.08)^2)) ) = 6.2 x 10^-6 7 failures: n = 8 x = 7 p = 0.8 n-x = 8-7 = 1 ( (8!) / (7!(1)!) ) x ( (0.08^7) x ((1-0.08)^1)) ) = 1.54 x 10^-7 8 failures: n = 8 x = 8 p = 0.8 n-x = 8-8 = 0 ( (8!) / (8!(0)!) ) x ( (0.08^8) x ((1-0.08)^0)) ) = 1.68 x 10^-9 f(6) = 6.21 x 10^-6 This study source was downloaded by from CourseH on :41:22 GMT -05:00 Stati sti cs - Portage Online Summer 2018 f(7) = 1.54 x 10^-7 f(8) = 1.68 x 10^-9 (6.21 x 10^-6) + (1.54 x 10^-7) + (1.68 x 10^-9) = 6.355x10^-6 Probability of 6,7, and 8 failing during an emergency = 6.36 x 10^-6 Answer Key A factory has eight safety systems. During an emergency, the probability of any one of the safety systems failing is .08. What is the probability that six or more safety systems will fail during an emergency?