Researchers believe that 6% of children have a gene that may be linked to a certain childhood disease.In an effort to track 50 of these children,researchers test 950 newborns for the presence of this gene.What is the probability that they find enough subjects for their study?
A)0.7912
B)0.1685
C)0.8315
D)0.8507
E)0.337

Question

Quizplus · Accepted Answer

The probability of any one newborn having the gene is 6% = 0.06. Therefore, the probability of any one newborn not having the gene is 1 - 0.06 = 0.94. We can treat this as a binomial distribution with n = 950 trials (newborns tested), and probability of success (finding a newborn with the gene) equal to 0.06. We want to find the probability of obtaining 50 or more successes (finding newborns with the gene).

Using a binomial probability calculator or software, we find that this probability is 0.8315, which is closest to option C (0.8315).

Researchers Believe That 6% of Children Have a Gene That