Question

Please write in bold letters

THANKS

In Lesson Six you've explored discrete probability distributions. To demonstrate your understanding of these, respond to the prompts below.

1. Describe an example of a real-world situation where the binomial distribution could be used to answer a question or solve a problem. Explain what makes this a binomial and how it could be used to answer the question that is being posed.
2. Based on the scenario you've created above, provide one possible set of values for n, x, p and q and work through the steps to calculate P(x). You may use technology to find factorials but show your work in all of the steps as you work towards an answer.
   1. Hint: Calculate nCr = ____fill in the blank, then calculate P(x = r) = ____fill in the blank.
3. Summarize your result above in a text statement relating the result to the scenario you described in #1.
4. Describe an original real-world example of a probability experiment. Identify the random variable and the possible values it could take on.
5. Describe an example off a discrete probability distribution. Explain how the example meets the criteria for a probability distribution. (

Answer 1

Answer:

Here, we have to discuss the real life example of binomial distribution. We know that binomial distribution is a discrete probability distribution.

Suppose you have your favourite football team X. You already know that the winning percentage of your favourite football team is 75%. That is, probability of winning for your favourite football team is p = 0.75.

Suppose your favourite team is going on domestic tournament where your team will play total six matches in first round. That is, we have n = 6 matches in first round.

For this situation, what is the probability that your favourite football team will win exact 5 matches in first round?

For answering above question we have to use binomial distribution.

For this binomial distribution, we have n = 6, p = 0.75

Binomial formula is given as below:

P(X=x) = nCx*p^x*(1 – p)^(n – x)

Here, we have to find P(X=5)

P(X=5) = 6C5*0.75^5*(1 – 0.75)^(6 – 5)

P(X=5) = 6*0.75^5*0.25^1

P(X=5) = 6* 0.237305*0.25

P(X=5) = 0.355958

Required probability = 0.3560

This means, there is a 35.6% possibility that your favorite football team will win exact 5 matches in the first round.

Original real world example of a probability experiment:

Probability of defective item in manufacturing industry is the real world example of a probability experiment. The random variable is number of defective items. Suppose company produces n items in a specific time interval and produces x defective items, then for this random or probability experiment, the probability of defective item is given as p = x/n.

Example of discrete probability distribution:

Binomial distribution or Poisson distribution is an example of discrete probability distribution. Consider probability of failure of car engine is 0.15 in long run travel. Suppose there are 10 cars participated in long run travel. Then what is the probability of failure of at least 5 car engines? For this scenario, we can use binomial distribution for answering this question.