Gull clutch size. Large black-tailed gulls usually lay one to three eggs, and rarely have a fourth egg clutch. It is thought that clutch sizes are effectively limited by how effectively parents can incubate their eggs. Suppose that on average, gulls have a \(25 \%\) of laying 1 egg, \(40 \%\) of laying 2 eggs, \(30 \%\) chance of laying 3 eggs, and \(5 \%\) chance of laying 4 eggs.

(a) Calculate the expected number of eggs laid by a random sample of 100 gulls.

(b) Calculate the standard deviation of the number of eggs laid by a random sample of 100 gulls.