The number of claims has the following distribution:

Number of claims 0 1 2 3 4

Probability 0.2 0.4 0.2 0.1 0.1

The claim sizes follow an exponential distribution with mean . The number of claims and the claim sizes are independent. Using the limited fluctuation (classical) credibility, determine the expected number of claims needed for aggregate losses to be within 5% of the expected aggregate losses with 90% probability.