on average 4speeding cases per day were recorded at cross what is the probability that exactly 5 s cases were recorded in any given day?

We use poisson distribution, with its probability formula:

e^(-x)*x^n/(n!), where x is the expected no. of occurence in a time interval, and n is the desired no. of occurence.
So the probability is e^(-4)*4^5/(5!) = 0.1563