Question

At the fencing center,60% of the fencers use foil as their main weapon. We randomly survey25 fencers at the fencing center, What is the probability that among the 25 surveyed, the number of fencers who use foil as their main weapon is

a). exactly 15

b.) at most 10

c.)more than 17

Answer 1

n = 25 sample size of 25 fencers     
p = 0.60 60% of the fencers use foil     
Let X be the number of fencers using foil as their main weapon      
X ~ Binomial distribution with n = 20 and p = 0.65      
       
a) To find P(X=15)      
We use the Excel function BINOM.DIST to find the probability      
P(X=15) = BINOM.DIST(15,25,0.60,FALSE)      
                 = 0.1612      
P(number of fencers using foil is exactly 15) = 0.1612      
       
b) To find P(number of fencers using foil is at most 10)      
that is to find P(X ≤ 10)      
We use the Excel function BINOM.DIST to find the probability      
P(X ≤ 10) = BINOM.DIST(10,25,0.60,TRUE)      
                 = 0.0344      
P(number of fencers using foil is at most 10) = 0.0344      
       
c) To find P(number of fencers using foil is more than 17)      
that is to find P(X > 17)      
P(X > 17) = 1 - P(X ≤ 16)      
We use the Excel function BINOM.DIST to find the probability      
P(X > 17) = 1 - BINOM.DIST(16,25,0.60,TRUE)      
                 = 1 - 0.7265      
                 = 0.2735      
P(number of fencers using foil is more than 17) = 0.2735