What is the probability that a respondent likes the Impossible burger?

Math 218-01 Quantitative Methods for Business, Midterm Exam #1A, Fall 2020

Dr. Matt Sequin


Instructions :

• This is an open book, open note exam. You may also use the internet for extra background information. However, you may not work with other students, tutors, or solicit assistance from other people via the internet. Submissions will be cross-checked with other students and with Blackboard’s internet scanning software. If any plagiarism is detected, the entire exam score will be a zero.

• Please write the exam out on separate pieces of paper. It is very important that the problems appear in order in your final submission. Please submit the exam by scanning it or by taking a legible picture of each page, then submitting it through Blackboard. Alternatively, you can email it to msequin@saintpeters.edu

• If a problem asks you to explain, be sure to give a thorough explanation in English sentences. For most of these problems, the explanation will be worth as much or more than getting the right numerical answer.

• The paper that you hand in should be a final draft. It should have everything written neatly in order with no cross outs, extra sentences written in the margins or other obvious edits.


Question Points Score 1 25 2 25 3 25 4 25


1. (25 points) Alfonso has just purchased a food truck to sell tacos. He will charge $3 per taco. The ingredients to make a taco cost $2.40, and the monthly costs of permits, gasoline and maintenance on the truck costs around $1500.

(a) Write out the revenue function R(X), the cost function C(x) and the profit func- tion P (X) for this situation. Briefly explain your answer.

(b) How many tacos will he have to sell to make a monthly profit of $1000? Briefly explain.

(c) Graph of the revenue function R(x) and the cost function C(x) on the same axis given below. Write out the (x, y) coordinates of their intersection point. Your graph should be drawn with a computer or be a very precise sketch.


2. (25 points) 400 people were participated in a taste test of two of the new ‘meatless’ burger patties: the Impossible Burger and the Beyond Burger. After recording their responses, the respondents were divided into the four groups in the table below.

Liked Beyond Disliked Beyond Liked Impossible 258 26

Disliked Impossible 21 95

(a) What is the probability that a respondent likes the Impossible burger? Explain.

(b) What is the probability that a respondent liked one burger but not the other? Explain.

(c) Given that someone liked the Beyond burger, what is the probability that they

also liked the Impossible burger? Explain.

[ P (I|B) = P (B ∩ I)

P (B)

] (d) Using your work above, if we know a person likes the Beyond burger, are they

more likely to like the Impossible burger than a randomly chosen respondent? Explain.


3. (25 points) Patty has applied for a business loan at the local bank to open a new independent coffee shop in town. The loan officer deciding whether or not to approve her needs to determine the probability her shop will become profitable in the next year. Unfortunately for Patty, the bank knows that there is a 40% chance of a Starbucks opening across the street from her proposed location. The bank estimates that if the Starbucks opens, she will only have a 15% chance of being profitable, but she will have a 60% chance if the Starbucks does not open.

(For all of the formulas below, let S be the event that Starbucks opens and let P be the event that Patty is profitable.)

(a) What is the probability that both Starbucks opens and she is profitable?

P (P ∩ S) = P (P |S) · P (S)

(b) Given all of this information, what is the probability that she is profitable? Show your work.

P (P ) = P (P |S)P (S) + P (P |SC)P (SC)

(c) What is the probability that either Starbucks opens or she is profitable (or both)?

P (P ∪ S) = P (S) + P (P )− P (P ∩ S)

(d) A year later, the loan officer hears that Patty’s coffee shop is profitable. What is the probability that the Starbucks opened across the street? Show your work.

P (S|P ) = P (S) · P (P |S) P (P )


4. (25 points) Banana is an electronics company. Most people who walk into the Banana store do not buy the most expensive phone: the MyPhone XX. The company did some data collection, and determined that one of their salesmen, Steve, can convince 20% of customers to buy a MyPhone XX. The store averages 100 customers on a typical day. (The formulas for the binomial and Poisson distributions are given below.)

P ({X = k}) = n! (k!)(n− k)!

(pk)(1− p)n−k

P ({X = k}) = λ k · e−λ


(a) Say that 100 customers enter the store during Steve’s shift. Use the binomial distribution to determine the probability that exactly 15 of them by a MyPhone XX. Show your work.

(b) Steve gets fired if he does not sell at least 2 MyPhone XXs on his shift. If 100 customers enter the store during his shift, use the binomial distribution to find the probability that he sells at least 2 MyPhone XXs. Explain what you did.

(c) Use the Poisson distribution to find the probability that exactly 100 customers enter the store. Explain what you did.

(d) Steve sometimes gets stressed about not selling his two phones because not enough customers come into the store. Use the Poisson distribution to estimate the probability that at least 2 customers enter the store on any given day. (There is no need to simplify your answer to a decimal.)


Calculate your paper price
Pages (550 words)
Approximate price: -

Why Work with Us

Top Quality and Well-Researched Papers

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

Professional and Experienced Academic Writers

We have a team of professional writers with experience in academic and business writing. Many are native speakers and able to perform any task for which you need help.

Free Unlimited Revisions

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account or by contacting our support.

Prompt Delivery and 100% Money-Back-Guarantee

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. In case you cannot provide us with more time, a 100% refund is guaranteed.

Original & Confidential

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text. We also promise maximum confidentiality in all of our services.

24/7 Customer Support

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

Calculate the price of your order

Total price:

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.


Essay Writing Service

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.


Admission Essays & Business Writing Help

An admission essay is an essay or other written statement by a candidate, often a potential student enrolling in a college, university, or graduate school. You can be rest assurred that through our service we will write the best admission essay for you.


Editing Support

Our academic writers and editors make the necessary changes to your paper so that it is polished. We also format your document by correctly quoting the sources and creating reference lists in the formats APA, Harvard, MLA, Chicago / Turabian.


Revision Support

If you think your paper could be improved, you can request a review. In this case, your paper will be checked by the writer or assigned to an editor. You can use this option as many times as you see fit. This is free because we want you to be completely satisfied with the service offered.