At The Fencing Center, 60% of the fencers use the foil as their main weapon. We randomly survey 25 fencers at The Fencing Center. We are interested in the number of fencers who do not use the foil as their main weapon.

  

a. In words, define the random variable X.

  

b. List the values that X may take on.

  

c. Give the distribution of X. X ~ _____(_____,_____)

  

d. How many are expected not to use the foil as their main weapon?

  

e. Find the probability that six do not use the foil as their main weapon.

  

f. Based on numerical values, would you be surprised if all 25 did not use foil as their main weapon? Justify your answer numerically.