5 Each week a sports team plays one home match and one away match. In their home matches they score goals at a constant average rate of 2.1 goals per match. In their away matches they score goals at a constant average rate of 0.8 goals per match. You may assume that goals are scored at random times and independently of one another.

1. A week is chosen at random.
   1. Find the probability that the team scores a total of 4 goals in their two matches.
   2. Find the probability that the team scores a total of 4 goals, with more goals scored in the home match than in the away match.
2. Use a suitable approximating distribution to find the probability that the team scores fewer than 25 goals in 10 randomly chosen weeks.
3. Justify the use of the approximating distribution used in part (b).