The owner of the Finer Diner submitted a proposal to you in hopes of selling the business to you. His asking price is $250,000. Your financial institution advises that your monthly payment to finance that amount would be $1850.00. This is in addition to other business expenses you would incur such as product, payroll, etc.
Upon reviewing the accounting records from the restaurant, you discover that it grosses roughly $3000 per day on 6 out of 10 days. Determine the estimated probability that the restaurant will gross over $3000:
A) On at least 4 out of 5 business days,
B) On at least 5 out of 10 business days,
C) On at least 7 out of 10 business days.
B) On at least 5 out of 10 business days,
To determine the estimated probability that the restaurant will gross over $3000 on different numbers of business days, we need to analyze the given information and make some calculations.
Given information:
- The restaurant grosses roughly $3000 per day on 6 out of 10 days.
Now, let's calculate the probabilities for each case:
A) On at least 4 out of 5 business days:
To calculate the probability of grossing over $3000 on at least 4 out of 5 business days, we need to consider the number of combinations that meet this condition. The possible combinations are:
- 4 days out of 5: C(5, 4) = 5
- 5 days out of 5: C(5, 5) = 1
Total combinations that meet the condition = 5 + 1 = 6
Total possible combinations for 5 business days = 2^5 = 32
Probability = Combinations that meet the condition / Total possible combinations
= 6 / 32
= 0.1875 or 18.75%
Therefore, the estimated probability that the restaurant will gross over $3000 on at least 4 out of 5 business days is 18.75%.
B) On at least 5 out of 10 business days:
To calculate the probability of grossing over $3000 on at least 5 out of 10 business days, we need to consider the number of combinations that meet this condition. The possible combinations are:
- 5 days out of 10: C(10, 5) = 252
- 6 days out of 10: C(10, 6) = 210
- 7 days out of 10: C(10, 7) = 120
- 8 days out of 10: C(10, 8) = 45
- 9 days out of 10: C(10, 9) = 10
- 10 days out of 10: C(10, 10) = 1
Total combinations that meet the condition = 252 + 210 + 120 + 45 + 10 + 1 = 638
Total possible combinations for 10 business days = 2^10 = 1024
Probability = Combinations that meet the condition / Total possible combinations
= 638 / 1024
≈ 0.623 or 62.3%
Therefore, the estimated probability that the restaurant will gross over $3000 on at least 5 out of 10 business days is approximately 62.3%.
C) On at least 7 out of 10 business days:
To calculate the probability of grossing over $3000 on at least 7 out of 10 business days, we need to consider the number of combinations that meet this condition. The possible combinations are:
- 7 days out of 10: C(10, 7) = 120
- 8 days out of 10: C(10, 8) = 45
- 9 days out of 10: C(10, 9) = 10
- 10 days out of 10: C(10, 10) = 1
Total combinations that meet the condition = 120 + 45 + 10 + 1 = 176
Total possible combinations for 10 business days = 2^10 = 1024
Probability = Combinations that meet the condition / Total possible combinations
= 176 / 1024
≈ 0.172 or 17.2%
Therefore, the estimated probability that the restaurant will gross over $3000 on at least 7 out of 10 business days is approximately 17.2%.