A hint to get started
Convert the hit count into a score
Teams of 8 people enter a shooting competition. Each member of a team takes a shot at the target. The number of points scored by a team is obtained by where is the number of shots that hit the target. For a particular team, each member of the team independently has a probability of 0.75 of hitting the target.
(i) Find the probability that a randomly chosen team scores more than 6 points.
(ii) Find the number of points that a team is most likely to score.
CJC · Discussion · Question 7
Translate the score condition into a condition on the hit count before using the distribution.