Question

6.3.3 From 2001 to 2011, in the United States the mean number of deaths of U.S. citizens by gun violence was about 11,849.73 with a standard deviation of 587.38, whereas the mean number of deaths by terrorism of U.S. citizens was 272.73 with a standard deviation of 801.61. This includes the acts of terrorism that happened on September 11. Assuming that the number of deaths by both gun violence and terrorism are normally distributed, answer the following questions. Source: U.S. Department of Justice

a. What is the probability that more than 11,000 U.S. citizens experienced death by gun violence from 2001 to 2011?

b. What is the probability that less than 10,000 U.S. citizens experienced death by gun violence from 2001 to 2011?

c. What is the probability that more than 300 U.S. citizens experienced deaths by terrorism from 2001 to 2011?

d. What is the probability that no more than 300 U.S. citizens experienced death by terrorism from 2001 to 2011?

Answer 1

Part a)

P ( X > 11000 ) = 1 - P ( X < 11000 )
Standardizing the value

Z = ( 11000 - 11849.73 ) / 587.38
Z = -1.45

P ( Z > -1.45 )
P ( X > 11000 ) = 1 - P ( Z < -1.45 )
P ( X > 11000 ) = 1 - 0.0735
P ( X > 11000 ) = 0.9265

Part b)

P ( X < 10000 )
Standardizing the value

Z = ( 10000 - 11849.73 ) / 587.38
Z = -3.15

P ( X < 10000 ) = P ( Z < -3.15 )
P ( X < 10000 ) = 0.0008

Part c)

P ( X > 300 ) = 1 - P ( X < 300 )
Standardizing the value

Z = ( 300 - 272.73 ) / 801.61
Z = 0.03

P ( Z > 0.03 )
P ( X > 300 ) = 1 - P ( Z < 0.03 )
P ( X > 300 ) = 1 - 0.512
P ( X > 300 ) = 0.488

Part d)

P ( X < 300 )
Standardizing the value

Z = ( 300 - 272.73 ) / 801.61
Z = 0.03

P ( X < 300 ) = P ( Z < 0.03 )
P ( X < 300 ) = 0.512