MATH 110 Module 4 Exam.| PORTGE LEARNING

MATH 110 Module 4 Exam.| PORTGE LEARNING Module 4 Exam Exam Page 1 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 Exam Page 3 A company manufactures a large number of rods. The lengths of the rods are normally distributed with a mean length of 3.7 inches and a standard deviation of .35 inches. If you choose a rod at random, what is the probability that the rod you chose will be: a) Less than 3.5 inches? z = (x-u) / o u = 3.7 o = 0.35 x = 3.5 (less than) x - u = 3.5 - 3.7 = -0.2 -0.2 / 0.35 = -0.5714 = -0.57 -0.57 on table = 0.28434 P(Z ≤ -0.57) = 0.28434 b) Greater than 3.5 inches? z = (x-u) / o u = 3.7 o = 0.35 x = 3.5 (greater than; 1-p(z≤...) x-u = 3.5 - 3.7 = -0.2 -0.2/0.35 = -0.5714 = -0.57 = (from table) 0.28434 1 - 0.28434 = 0.71566 P(Z ≥ -0.57) = 0.71566 c) Between 3.4 inches and 4 inches?