QUESTION 2

2.1. 60% of the players at a Spanish football club are local. Past experience has shown that 10% of local players have disciplinary issues and are suspended during a season, while 20% of overseas players have disciplinary issues leading to suspension. A player has just been suspended due to ill-discipline. Determine the probability that this player was from overseas. 

2.2. Cancer patients arrive at an oncology centre at an average rate of 5 patients per hour. Assuming a Poisson distribution, determine the probability that: 

2.2.1. at least two cancer patients arrive in a given hour.

2.2.2. four cancer patients arrive in a given half-hour period. 

2.3. The average lifetime of a particular brand of car battery is 3 years with a standard deviation of 6 months. Assuming these lifetimes are normally distributed, calculate the:

2.3.1. percentage of these batteries that last more than 4 years.

2.3.2. maximum lifetime of a battery to be in the 10% of batteries with the shortest lifetime.