X, the number of foxes the Easter Bunny sees in the forest on a given day, is Poisson distributed. During the seven days of Week 5, Mr Bunny saw respectively \(1,5,4,7,3,2\), and 8 foxes. By an odd coincidence, \(\mu_{X}\) and the average number of foxes in Week 5 are exactly the same. Calculate \(\mu_{X}\), and use that to answer the following questions.

(a) What is \(\lambda\) ?

(b) What is \(\sigma_{X}\) ?

(c) What is the probability that the Easter Bunny will see precisely five foxes today?