Final answer:
To estimate the number of asymptomatic carriers in a population of humans suffering from cystic fibrosis, the Hardy-Weinberg equation can be used. Based on a given frequency of the disease allele, we can calculate the frequency of carriers and then estimate the number of carriers in the population.
Step-by-step explanation:
The Hardy-Weinberg equation can be used to estimate the number of asymptomatic carriers in a population. In this scenario, we are given that 1 in 2000 individuals suffer from cystic fibrosis, which is an autosomal recessive disease. To calculate the frequency of carriers (heterozygotes) in the population, we can use the equation:
p^2 + 2pq + q^2 = 1
where p is the frequency of the dominant allele (normal allele) and q is the frequency of the recessive allele (disease allele). Since cystic fibrosis is recessive, q^2 represents the frequency of affected individuals. We are given that 1 in 2000 individuals have the disease, so q^2 = 1/2000. Solving for q, we find q ≈ 0.0224.
Since q = frequency of carriers (2pq), we can substitute q into the equation to solve for p. 2p(0.0224) = frequency of carriers. Solving for p, we find p ≈ 0.9776.
To calculate the estimated number of asymptomatic carriers in the population, we multiply the frequency of carriers by the total population size. Assuming the population size is 10,000 individuals, the estimated number of asymptomatic carriers would be 0.9776 * 10,000 ≈ 9776.
Therefore, the correct answer is 9776 carriers.