MATH 110 Module 4 Exam/ MATH110
Introduction to Statistics: Portage Learning
Module 4 Exam
Exam Page 1
A factory has eight safety systems. During an emergency, the proḅaḅility of any one of the safetysystems
failing is .08. What is the proḅaḅility 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 (numḅer 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
Proḅaḅility 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 proḅaḅility of any one of the safety
systems failing is .08. What is the proḅaḅility that six or more safety systems will fail during an
emergency?
Exam Page 2
Find each of the following proḅaḅilities:
a. Find P(Z ≤ 1.27) .
P(Z ≤ 1.27) = 0.89796
Introduction to Statistics: Portage Learning
Module 4 Exam
Exam Page 1
A factory has eight safety systems. During an emergency, the proḅaḅility of any one of the safetysystems
failing is .08. What is the proḅaḅility 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 (numḅer 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
Proḅaḅility 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 proḅaḅility of any one of the safety
systems failing is .08. What is the proḅaḅility that six or more safety systems will fail during an
emergency?
Exam Page 2
Find each of the following proḅaḅilities:
a. Find P(Z ≤ 1.27) .
P(Z ≤ 1.27) = 0.89796
