WORKSHEET #16a
ST 350
Reiland
Name
Concussions, cancer, and earthquakes
1. Recent NCAA football concussion statistics show that concussions occur at a rate of !Þ#(
concussions for every 100 game participants. In a game between NCSU and UNC in which a
total of 65 players particpate, find the probability of ! concussions, " concussion, and 2
concussions in the game.
mean concussion rate in game with 65 particpants: - œ
:ÐBÑ œ
/ - - B
Bx ß
:Ð!Ñ œ
/!Þ"(&& Ð!Þ"(&&Ñ!
!x
œ !Þ)$*
:Ð"Ñ œ
/!Þ"(&& Ð!Þ"(&&Ñ"
"x
œ !Þ"%(#&
:Ð#Ñ œ
/!Þ"(&& Ð!Þ"(&&Ñ#
#x
œ !Þ!"#*#
'&
"!! !Þ#(
œ !Þ"(&&
B œ !ß "ß #ß $ß %ß ÞÞÞ
2. Camp Lejeune in North Carolina has been identified as having a suspicious cluster of 60
cases of a rare form of cancer (the drinking water at Camp Lejeune was contaminated for 35
years by leaking gasoline tanks on the base and by leaking tanks at a dry cleaner store across
from the base). The U.S. rate for this type of cancer is 5 per 100,000 people. If over the
years 700,000 people were exposed at Camp Lejeunne, what is the probability that 60 or
more cases of this cancer would occur?
mean cancer rate for 700,000: - œ ( ‚ & œ $&
T Ð\ '!Ñ œ "  T Ð\ Ÿ &*Ñ œ "  !Þ**** œ !Þ!!!" (using ti83/84).
Therefore, at the U.S. rate for this cancer, 60 or more cases is very rare. This very small
probability of 60 or more cancer cases is evidence that the rate of this rare form of cancer is
much higher at Camp Lejeune.
3. For a recent period of 100 years, there were 93 major earthquakes (at least 6.0 on the Richter
scale) in the world (based on data from the World Almanac and Book of Facts). Use the
Poisson distribution to find the probability that the number of major earthquakes in a
randomly selected year is:
a. 0 b. 1 c. 2 d. 3
*$
mean number of major eathquakes per year: - œ "!!
œ !Þ*$
actual results
:Ð!Ñ œ
:Ð"Ñ œ
:Ð#Ñ œ
:Ð$Ñ œ
/!Þ*$ Ð!Þ*$Ñ!
!x
/!Þ*$ Ð!Þ*$Ñ"
"x
/!Þ*$ Ð!Þ*$Ñ#
#x
/!Þ*$ Ð!Þ*$Ñ$
$x
œ !Þ$*&
0 major earthquakes: 47 years
œ !Þ$'(
1 major earthquakes: 31 years
œ !Þ"("
2 major earthquakes: 13 years
œ !Þ!&$
3 major earthquakes: 5 years