Claims arrive at a branch of an insurance company according a homogeneous Poisson process with an intensity of \(\lambda=0.4\) per working hour. The claim size \(Z\) has an exponential distribution so that \(80 \%\) of the claim sizes are below \(\$ 100000\), whereas \(20 \%\) are equal or larger than \(\$ 100000\).

(1) What is the probability that the fourth claim does not arrive in the first two working hours of a day?

(2) What is the mean size of a claim?

(3) Determine approximately the probability that the sum of the sizes of 10 consecutive claims exceeds \(\$ 800000\).