16. Dominant Traits The alleles for black (B) and white

(b) feather color in chickens show incomplete dominance; individuals with the gene pair Bb have

“blue” feathers. When one individual that is homozygous dominant (BB) for this trait is mated with an individual that is homozygous recessive (bb) for this trait, 1/2 will carry the gene pair Bb. Let x be the number of chicks with “blue” feathers in a sample of n520 chicks resulting from this type of cross.

a. Does the random variable x have a binomial distribution?

If not, why not? If so, what are the values of n and p?

b. What is the mean number of chicks with “blue”

feathers in the sample?

c. What is the probability of observing fewer than five chicks with “blue” feathers?

d. What is the probability that the number of chicks with “blue” feathers is greater than or equal to 10 but less than or equal to 12?