Can you tell the difference? Is this a Binomial or Hypergeometric Model? 1. At a certain manufacturing company, approximately 5% of the products are defective. We are interested in calculating the probability that the third defective is the 20th one sampled. 2. An assembly line produces products that they put into boxes of 50. The inspector then randomly picks 3 items inside a box to test to see if they are defective. In a box containing 4 defectives, they are interested in the probability that at least one of the three items sampled is defective. 3. In a capture-recapture experiment, 20 animals were captured, tagged and released. A few weeks later, a sample of 40 of these animals is capture and we are interested in the number of animals in our sample that are tagged. 4. A husband has 7 tasks on his to-do list and a wife has 10 things on her to-do list. Five tasks are randomly picked out of these 17 tasks. We are interest in the expected number of tasks the wife will have to do. 5. A certain stoplight, when coming from the North, is green approximately 31% of the time. Over the next few days, someone comes to this light 8 times from the North. We are interested in finding the expected number of green lights the person will come to. 6. A police officer has found that approximately 15% of the vehicles he pulls over are from out of state. We are interested in the number of vehicles that are out of state from the next 50 vehicles that he pulls over.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Can you tell the difference? Is this a Binomial or Hypergeometric Model?
1. At a certain manufacturing company, approximately 5% of the products are defective. We are interested in calculating the
2. An assembly line produces products that they put into boxes of 50. The inspector then randomly picks 3 items inside a box to test to see if they are defective. In a box containing 4 defectives, they are interested in the probability that at least one of the three items sampled is defective.
3. In a capture-recapture experiment, 20 animals were captured, tagged and released. A few weeks later, a sample of 40 of these animals is capture and we are interested in the number of animals in our sample that are tagged.
4. A husband has 7 tasks on his to-do list and a wife has 10 things on her to-do list. Five tasks are randomly picked out of these 17 tasks. We are interest in the expected number of tasks the wife will have to do.
5. A certain stoplight, when coming from the North, is green approximately 31% of the time. Over the next few days, someone comes to this light 8 times from the North. We are interested in finding the expected number of green lights the person will come to.
6. A police officer has found that approximately 15% of the vehicles he pulls over are from out of state. We are interested in the number of vehicles that are out of state from the next 50 vehicles that he pulls over.
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