Math 218 01 Quantitative Methods For Business Midterm Exam

Math 218 01 Quantitative Methods For Businessmidterm Exam 1a Fall

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Compose a comprehensive academic paper that addresses each of the following questions based on the cleaned assignment instructions:

1. Alfonso’s Food Truck Business Analysis:
   • Define the revenue function R(x), cost function C(x), and profit function P(x) for Alfonso’s food truck business, where he charges $3 per taco, each taco costs $2.40 to make, and fixed monthly costs are $1500. Include a brief explanation of your functions.
   • Determine how many tacos Alfonso must sell to achieve a monthly profit of $1000. Explain your method.
   • Graph the revenue and cost functions on the same coordinate axes, and identify the (x, y) coordinates of their intersection point. Describe how the graph should be drawn and the significance of the intersection point.
2. Burger Taste Test Probability Analysis:
   • Given data from a taste test where 258 participants liked the Beyond Burger and 21 disliked it, while 26 liked the Impossible Burger and 95 disliked it, answer the following:
     1. Calculate the probability that a respondent likes the Impossible burger. Provide your explanation.
     2. Calculate the probability that a respondent liked one burger but not the other. Explain your reasoning.
     3. Determine the probability that a respondent liked the Impossible burger given that they liked the Beyond burger, using the conditional probability formula P(I|B) = P(B ∩ I) / P(B). Explain your calculation.
     4. Based on your previous calculation, assess whether someone who liked the Beyond burger is more likely to also like the Impossible burger than a randomly chosen respondent. Explain your reasoning.
3. Patty’s Coffee Shop Loan Probability Scenarios:
   • Patty applies for a business loan, and the bank estimates:

     - Probability that a Starbucks opens across the street: 40%

     - Probability Patty's shop is profitable if Starbucks opens: 15%

     - Probability Patty's shop is profitable if Starbucks does not open: 60%

     1. Calculate the probability that both Starbucks opens and Patty's shop is profitable.
     2. Determine the probability that Patty's shop is profitable, using the total probability theorem. Show your work step by step.
     3. Find the probability that either Starbucks opens or Patty's shop is profitable (or both). Demonstrate your calculation.
     4. After one year, given that Patty’s shop is profitable, compute the probability that Starbucks opened. Include your calculation process.
4. Electronics Store Sales Analysis Using Binomial and Poisson Distributions:
   • Most customers do not buy the most expensive phone, the MyPhone XX. Steve, a salesman, can convince 20% of customers to buy it. On a day with 100 customers:
     1. Using the binomial distribution, calculate the probability that exactly 15 customers buy the MyPhone XX. Show your work.
     2. Determine the probability that Steve sells at least 2 MyPhone XXs during his shift. Explain your approach.
     3. Using the Poisson distribution, find the probability that exactly 100 customers enter the store in a day and explain your method.
     4. Estimate the probability that at least 2 customers enter the store on any given day using the Poisson distribution. No need to simplify your answer.

In your paper, be sure to provide clear explanations, demonstrate all calculations thoroughly, include relevant formulas, and interpret the results in the context of each problem. Use appropriate academic writing standards and cite credible sources as needed.

References

• Albright, S. C., Winston, W. L., & Zuo, M. (2014). Data analysis and decision making. Cengage Learning.
• Devore, J. L. (2015). Probability and statistics for engineering and the sciences. Cengage Learning.
• Moore, D. S., McCabe, G. P., & Craig, B. A. (2017). Introduction to the practice of statistics. W. H. Freeman.
• Ross, S. M. (2014). Introduction to probability models. Academic press.
• Wasserman, L. (2013). All of statistics: a concise course in statistical inference. Springer Science & Business Media.
• Wooldridge, J. M. (2013). Introductory econometrics: a modern approach. Cengage Learning.
• Strauss, S. M., & Howe, C. (2012). Statistics for business: Data analysis and statistical inference. McGraw-Hill Education.
• Feller, W. (2008). An introduction to probability theory and its applications. Wiley.
• Gerald, G., & Sullivan, J. (2013). Statistics for business and economics. Pearson.
• Hogg, R. V., & Tanis, E. A. (2015). Probability and statistical inference. Pearson.