Large black-tailed gulls usually lay one to three eggs, and rarely have a fourth egg clutch. It is thought that clutch sizes are limited by how effectively parents can incubate their eggs. Suppose that on average, gulls have a 24.1% of laying 1 egg, 32% of laying 2 eggs, 9.1% chance of laying 3 eggs, and 34.8% chance of laying 4 eggs. What is the variance of the number of eggs laid by a random sample of 100 gulls? Round your answer to five decimal place