half = 50%. Really!

The police force is the total group of individuals. I understand the sentences as "a lot of" the police officers have examined X. It could also mean 50% of the police officers have examined it. Sometimes people use "half" just to mean a large number, not an exact half, and that's how I think it is in your sentence. "Half the people at that meeting didn't understand the problem" just might refer to a lot of them.