For this particular distribution you can just multiply the parameter by 7 to get the distribution of accidents over 7 days. Depending on your level of study you should learn that as a fact or be able to prove it. (im guessing you need to learn it, not prove it).
so if X is acidents over 7 days,
You should be able to do now that you have the distribution
If the sum is >420 then the average is >3.3333. Have you been taught an approximate distribution for sample averages? (Hint: Think "central limit theorum")