MATH 110 MODULE 4 EXAM 2023/2024 QUESTIONS AND
ANSWERS- PORTAGE 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
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?
Exam Page 2
Find each of the following probabilities:
a. Find P(Z ≤ 1.27) .
P(Z ≤ 1.27) = 0.89796
ANSWERS- PORTAGE 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
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?
Exam Page 2
Find each of the following probabilities:
a. Find P(Z ≤ 1.27) .
P(Z ≤ 1.27) = 0.89796
