Final answer:
Using the Hardy-Weinberg principle, we find that the carrier frequency of sickle cell anemia in the African-American population is approximately 1 in 10.
Step-by-step explanation:
The disease frequency for sickle cell anemia in the African-American population is 1 in 400. To determine the carrier frequency, we apply the Hardy-Weinberg principle which states that if p represents the frequency of the dominant allele and q represents the frequency of the recessive allele in the population, then the frequency of the genotype for carriers (heterozygotes) would be 2pq. As sickle cell anemia is an autosomal recessive disorder, individuals with the disease have a genotype of qq (homozygous recessive). The square root of the disease frequency (1/400) gives us the q value (the frequency of the recessive allele), then we can use the Hardy-Weinberg equation to find 2pq. The calculation is as follows: q = √(1/400) = 1/20, where p is approximately 1 (as the dominant allele is much more common than the recessive one), and thus 2pq is approximately 2 * (1/20) * 1 = 1/10.
The carrier frequency of sickle cell anemia in the African-American population is therefore about 1 in 10.