In a computer game, a canon can fire shots at a distance ofX~N(µ=10cm, =2cm). A
ID: 2917727 • Letter: I
Question
In a computer game, a canon can fire shots at a distance ofX~N(µ=10cm, =2cm). A tank with length 2 cm comes towardthe cannon.a) If the distance of the front of the tank to the cannon is 8 cm,please compute the probability that the cannon will hit the body ofthe tank in one shot.
b) Please find the best distance between the front of the tank andthe cannon at which the cannon will have the greatest chance to hitthe tank body in one shot.
Explanation / Answer
mean, µ=10cm, standard deviation, =2cm a) probability that the cannon will hit the body of the tank in oneshot If the distance of the front of the tank to the cannon is 8 cm=P(X=8) =P((X-)/ =(8-10)/2) =P(Z=-1) =0.1587 b) for the cannon to have the greatest chance to hit the tank bodyin one shot, probability should be 1 hence, for p =1, from the table z should be more than 3.4 hence , z>3.4 so, (X-)/ > 3.4 so, (X-10)/2 >3.4 hence, X> 16.8 best distance between the front of the tank and the cannon at whichthe cannon will have the greatest chance to hit the tank body inone shot is 16.8