You travel with 2 business associates to Las Vegas for a professional conference
ID: 3253394 • Letter: Y
Question
You travel with 2 business associates to Las Vegas for a professional conference on new fast-food franchise concepts. Your success in business has brought you in contact with these individuals--an attorney and a CPA. They are what is referred to as "Smart Money": individuals that have special knowledge of a particular business and ready investment capital, in this case, to invest in fast-food franchise operations. After a number of meetings with franchisors pitching their concepts, your team settles on considering a very interesting idea for Indian Deli/Fast-Food. Upon your return to Williamsburg, VA. you contact your banker about the business trip. She is also intrigued by the idea, but acknowledges that the concept is best suited for large urban centers. She calls a meeting with the group to discuss potential capital investment in the idea. She directs several questions in advance to the group that she would like answered at the meeting to support the financing: (use the best available distribution from our readings)
1) The banker suggests that it is essential that at least 75% of the stores opened succeed 3 years of operation for the financing to be acceptable. (Success is defined as a store is profitable and still open for business for 3 years.) You believe that the 3 year survival rate for a store is 0.50 and consider opening 16 test stores in the Charlotte, NC area. What is the probability that between 12 and 16 stores will be successful after 3 years?
2) Related to question 1), what is the probability that fewer than 5 stores will be open after 3 years of operation.
3) The distribution of annual revenue is estimated to be between $2.5 M dollars and $6.5 M dollars. Additionally, there is no way to know if any particular level of revenue is more or less likely than another. What is the probability of annual revenue being more than or equal to $3.0 M dollars.
4) In a discussion with the franchisor, he estimates that the average hourly number of customers arriving during the mid-day part of the day (12:00 a.m.--3:00 p.m.) is 220/hr. What is probability of 300 or more arrivals occurring in the first hour of this day part (11:00-12:00)?
5) If the value of a customer purchase is estimated to be normally distributed with a mean of $4.50 and standard deviation of $3.50, what is the probability of a customer purchase being more than $8.00?
Explanation / Answer
Answer:
1) The banker suggests that it is essential that at least 75% of the stores opened succeed 3 years of operation for the financing to be acceptable. (Success is defined as a store is profitable and still open for business for 3 years.) You believe that the 3 year survival rate for a store is 0.50 and consider opening 16 test stores in the Charlotte, NC area. What is the probability that between 12 and 16 stores will be successful after 3 years?
p=0.5, n=16, binomial distribution used.
P(X=x) = (nCx) px (1-p)n-x
P( 12<x<16) = P(x=13)+P( x=14)+P(x=15) =0.0085+0.0018+0.0002
=0.0106
Binomial Probabilities Table
X
P(X)
13
0.0085
14
0.0018
15
0.0002
2) Related to question 1), what is the probability that fewer than 5 stores will be open after 3 years of operation.
P( x <5) = P(x=0)+P( x=1)+P(x=2)+ P(x=3)+P( x=4)
=0.0000+0.0002+0.0018+0.0085+0.0278
=0.0383
Binomial Probabilities Table
X
P(X)
0
0.0000
1
0.0002
2
0.0018
3
0.0085
4
0.0278
3) The distribution of annual revenue is estimated to be between $2.5 M dollars and $6.5 M dollars. Additionally, there is no way to know if any particular level of revenue is more or less likely than another. What is the probability of annual revenue being more than or equal to $3.0 M dollars.
Uniform distribution used.
a=2.5, b=6.5
P( x >3.0)=0.875
4) In a discussion with the franchisor, he estimates that the average hourly number of customers arriving during the mid-day part of the day (12:00 a.m.--3:00 p.m.) is 220/hr. What is probability of 300 or more arrivals occurring in the first hour of this day part (11:00-12:00)?
average hourly number of customers arriving during the mid-day part of the day (12:00 a.m.--3:00 p.m.) is 220/hr
average arrival =220/hr
Poisson distribution used.
P( x 300) =0.0000
5) If the value of a customer purchase is estimated to be normally distributed with a mean of $4.50 and standard deviation of $3.50, what is the probability of a customer purchase being more than $8.00?
Z value of 8, z =(8-4.5)/3.5 =1
P( x >8) = P( z >1)
=0.1587
Binomial Probabilities Table
X
P(X)
13
0.0085
14
0.0018
15
0.0002
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.