Cast and Retrieve Fishing is a popular technique. Thereby, the lure is casted to the target,

letting it fall to the desired depth. Thereafter, the lure is retrieved by reeling, pulling the line

in order to mimic a moving bait. This action entices a bite by a targeted fish. If there is a bite

(retrieve is successful), the fish is pulled out and unhooked. Thereafter the procedure is repeated.

Assume that in a sequence ofnNattempts thei-th retrieve success is modeled by the eventAi

whereas the weight (in kg) of the potential catch is described by a random variableXi. Suppose

that{Ai,Xj:i= 1,...,n,j= 1,...,n}are independent and the probability ofAiis1for12

i= 1,...,nwhereas the fish weightXjfor eachj= 1,...,nfollows a Gamma distribution with shape parameter= 3 and scale parameter= 2. Estimate the probability to catch more than 7kg fish withinn= 12 attempts.

(Hint:give the result asN(0,1)(] , x]) with explicitly determinedxR.)