Hey, I need help with a binomial distribution question.
Q: Scientists collecting butterfly samples near a nuclear power plant found that wing and antenna defects were somewhat common. Of 98 butterflies collected in the sampling, 3 showed at least 1 defect. If a previous study on butterflies found near the same nuclear power plant thirty years ago found that there was 1 defect per 1000 butterfly, what is the probability of finding7 in a sample of 98?
I'm assuming the way to approach this question is finding ?(X=7∣X≥3)when X∼bin(98,1/1000)? When I do so and plug the numbers into the binomial distribution equation like so:
P (X=k) = (98!/(7!(98-7)!))(0.0017)(1-0.001)98-7
I get the answer 1.263x10-11. I'm not sure if this is the right answer, and if so I'm not sure how to interpret the answer. Any help would be great.
Q: Scientists collecting butterfly samples near a nuclear power plant found that wing and antenna defects were somewhat common. Of 98 butterflies collected in the sampling, 3 showed at least 1 defect. If a previous study on butterflies found near the same nuclear power plant thirty years ago found that there was 1 defect per 1000 butterfly, what is the probability of finding7 in a sample of 98?
I'm assuming the way to approach this question is finding ?(X=7∣X≥3)when X∼bin(98,1/1000)? When I do so and plug the numbers into the binomial distribution equation like so:
P (X=k) = (98!/(7!(98-7)!))(0.0017)(1-0.001)98-7
I get the answer 1.263x10-11. I'm not sure if this is the right answer, and if so I'm not sure how to interpret the answer. Any help would be great.