(Solved): At The Fencing Center, \( 60 \% \) of the fencers use the foil as their main weapon. We randomly su ...

At The Fencing Center, \( 60 \% \) of the fencers use the foil as their main weapon. We randomly survey 22 fencers at The Fencing Center. We are interested in the numbers that do not use the foil as their main weapon. Part (a) In words, define the Random Variable \( X \); the number of fencers that do use the foil as their main weapon the number of fencers at The Fencing Center the different types of weapons the number of fencers that do not use the foil as their main weapon Correct This is a numerical measure of the outcome of the survey. Part (b) List the values that \( X \) may take on. \[ \begin{array}{l} x=0,1,2, \ldots, 60 \\ x=0,1,2, \ldots, 22 \\ x=1,2,3, \ldots, 22 \\ x=1,2,3, \ldots, 60 \end{array} \] Part (c) Give the distribution of \( X \). \( x-(1+) \) Part (d) How many fencers are expected to not use the foil as thair main weapon? (Round your answer to the nearest whole numbec) fencers Part (e) Find the probability that twelve do not use the foil as their main weapon. (Round your answer to four decimai places.) Part (f) Based on numerical values, would you be surprised if all 22 did not use foil as their main weapon? Yes. The probabilty of all 22 fencers not using the foil as their main weapon is small (fless than 196). No. The probablity of all 22 fencers not using the foil as their main weapon is large (more than \( 10 \% \) ).