In the discussion forum for this week, you will create a scenario that requires the use of a binomial distribution.
· For your post you will make up a problem that uses binomial distribution similar to the example below. Try to have 3 scenarios. You do not need to solve your own problem.
· If you can, try a probability different from .5. In your problem, make sure that the probability stays the same for each trial!
· Example:
· For this example, assume that a family has 8 children, and the probability that any one child is a boy is .51.
· a) Find the probability that the family has exactly 5 boys.
· b) Find the probability that the family has more than 5 boys.
· c) Find the probability that the family has at most 5 boys.
Struggling with where to start this assignment? Follow this guide to tackle your assignment easily!
🔹 Scenario 1: Call Center Success Rate
A call center operator makes 12 calls in one hour. Each call has a 30% chance of resulting in a successful sale.
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a) Find the probability that the operator makes exactly 4 sales.
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b) Find the probability that the operator makes more than 6 sales.
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c) Find the probability that the operator makes at most 2 sales.
🔹 Scenario 2: Basketball Free Throws
A basketball player has a free throw success rate of 75%. In a practice session, she attempts 10 free throws.
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a) Find the probability that she makes exactly 8 free throws.
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b) Find the probability that she makes fewer than 6 free throws.
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c) Find the probability that she makes all 10 free throws.
🔹 Scenario 3: Quality Control in a Factory
In a factory, the probability that a produced light bulb is defective is 0.08. An inspector checks a random sample of 20 bulbs.
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a) Find the probability that exactly 3 bulbs are defective.
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b) Find the probability that no more than 2 bulbs are defective.
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c) Find the probability that more than 5 bulbs are defective.
👉 These follow the binomial conditions:
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Fixed number of trials (n).
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Only two outcomes (success/failure).
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Constant probability of success (p).
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Independent trials.
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