A homozygous plant with 20 cm diameter flowers is crossed with a homozygous plant of the same species that has a 40cm diameter flowers. The F1 plants all have flowers 30cm in diameter. In the F2 generation of 512 plants, 2plants have flowers 20 cm in diameter, 2 plants have flowers 40cm in diameter, and the remaining 508 plants have flowers of a range of sizes in between.

a) assuming that all alleles involved act additively, how many genes control flower size in this plant?

b)calculate the mean, variance, and standard deviation for flower diameter in the backcross progency.