Question

In: Statistics and Probability

Please write in bold letters THANKS In Lesson Six you've explored discrete probability distributions. To demonstrate...

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. (

Solutions

Expert Solution

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.


Related Solutions

Please write in BOLD Thanks :) In Lesson Eight you've learned how to construct confidence intervals...
Please write in BOLD Thanks :) In Lesson Eight you've learned how to construct confidence intervals for population parameters and proportions, based on data from samples. In a short paragraph, distinguish between Sampling Error and the Margin of Error. Explain what each represents and the relationship between them. In a short paragraph, distinguish between a Point Estimate and an Interval Estimate. Explain what each represents and the relationship between them. In a short paragraph, distinguish between a Confidence Interval and...
Please write in BOLD Thanks :) In Lesson Eight you've learned how to construct confidence intervals...
Please write in BOLD Thanks :) In Lesson Eight you've learned how to construct confidence intervals for population parameters and proportions, based on data from samples. In a short paragraph, distinguish between Sampling Error and the Margin of Error. Explain what each represents and the relationship between them. In a short paragraph, distinguish between a Point Estimate and an Interval Estimate. Explain what each represents and the relationship between them. In a short paragraph, distinguish between a Confidence Interval and...
Please write in Bold letters thanks In a sentence or two each, provide examples of each...
Please write in Bold letters thanks In a sentence or two each, provide examples of each of the following terms and explain why the example illustrates the related concept. Do not use examples from the text but use critical thinking to make up your own. (1 point each) Independent events Dependent events Complementary events Union of events Intersection of events
write in Bold letters thanks Two types of medication for hives are being tested. The manufacturer...
write in Bold letters thanks Two types of medication for hives are being tested. The manufacturer claims that the new medication B is more effective than the standard medication A and undertakes a comparison to determine if medication B produces relief for a higher proportion of adult patients within a 30-minute time window. 20 out of a random sample of 200 adults given medication A still had hives 30 minutes after taking the medication. 12 out of another random sample...
The binomial and Poisson distributions are two different discrete probability distributions. Explain the differences between the...
The binomial and Poisson distributions are two different discrete probability distributions. Explain the differences between the distributions and provide an example of how they could be used in your industry or field of study. In replies to peers, discuss additional differences that have not already been identified and provide additional examples of how the distributions can be used.
The binomial and Poisson distributions are two different discrete probability distributions. Explain the differences between the...
The binomial and Poisson distributions are two different discrete probability distributions. Explain the differences between the distributions and provide an example of how they could be used in your industry or field of study.
discrete probability distributions There are 37 different processors on the motherboard of a controller. 6 of...
discrete probability distributions There are 37 different processors on the motherboard of a controller. 6 of the processors are faulty. It is known that there are one or more faults on the motherboard. In an attempt to locate the error, 7 random processors are selected for testing. tasks a) Determine the expected number of defective processors. Round your answer to 2 decimal places. b) Determine the variance of the number of defective processors. Round your answer to 4 decimal places....
What is probability distribution? a. Select 5 probability distributions from discrete and continuous random varibles. Express...
What is probability distribution? a. Select 5 probability distributions from discrete and continuous random varibles. Express the probability function and distribution functions of these distributions. b. Show that the distributions you select fulfill the conditions for the probability functions to be probability functions. c. Find the expected values and variance of these distributions theoretically.
Expected Returns: Discrete Distribution The market and Stock J have the following probability distributions: Probability rM...
Expected Returns: Discrete Distribution The market and Stock J have the following probability distributions: Probability rM rJ 0.3 12% 21% 0.4 10 4 0.3 17 12 a.Calculate the expected rate of return for the market. Round your answer to two decimal places. % b. Calculate the expected rate of return for Stock J. Round your answer to two decimal places. % c. Calculate the standard deviation for the market. Round your answer to two decimal places. % d. Calculate the...
Expected Returns: Discrete Distribution The market and Stock J have the following probability distributions: Probability rM...
Expected Returns: Discrete Distribution The market and Stock J have the following probability distributions: Probability rM rJ 0.3 14% 18% 0.4 9 7 0.3 19 12 Calculate the expected rate of return for the market. Round your answer to two decimal places. % Calculate the expected rate of return for Stock J. Round your answer to two decimal places. % Calculate the standard deviation for the market. Do not round intermediate calculations. Round your answer to two decimal places. %...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT