Perry is considering trying to open a new business within the next few years, and he is wondering what kind of businesses tend to be successful. So far, he has compiled two tables. The first table shows the number of businesses of several types started in Perry's city over the course of two years, and the number which did not succeed and were forced to shut down within two years of opening. The second table shows the records of successful new businesses, showing how much profit those new businesses made. Businesses on the boundary lines fall in the lower category.
| Type | Food | Retail | Financial | Service |
| --------- | ------ | ------ | --------- | ------- |
| Opened | 3,193 | 2,280 | 1,898 | 5,045 |
| Closed | 1,977 | 1,626 | 1,443 | 3,548 |
| | | | | |
| | Up to $25k | $25-50k | $50-75k | $75-100k | Over $100k |
| Food | 945 | 623 | 601 | 258 | 114 |
| Retail | 813 | 548 | 347 | 188 | 63 |
| Financial | 316 | 244 | 195 | 86 | 51 |
| Service | 979 | 739 | 432 | 174 | 124 |
Using the tables as experimental data, determine whether it is more likely for a new food business to succeed than a new service business.
Answer (2)
Calculate the success rate for food businesses: S F = 3193 3193 − 1977 ≈ 0.3808 .
Calculate the success rate for service businesses: S S = 5045 5045 − 3548 ≈ 0.2967 .
Compare the success rates: 0.2967"> 0.3808 > 0.2967 .
A new food business is more likely to be successful: Food .
Explanation
Analyze the problem Let's analyze the data to determine whether a new food business or a new service business is more likely to be successful. We'll calculate the success rate for each type of business based on the provided data.
Explain the success rate calculation The success rate is calculated as the number of businesses that remained open (i.e., did not close) divided by the total number of businesses opened. For food businesses, the number opened is 3,193 and the number closed is 1,977. For service businesses, the number opened is 5,045 and the number closed is 3,548.
Calculate the success rate for food businesses The success rate for food businesses ( S F ) is calculated as: S F = Number Opened Number Opened − Number Closed = 3193 3193 − 1977 S F = 3193 1216 ≈ 0.3808 So, approximately 38.08% of food businesses are successful.
Calculate the success rate for service businesses The success rate for service businesses ( S S ) is calculated as: S S = Number Opened Number Opened − Number Closed = 5045 5045 − 3548 S S = 5045 1497 ≈ 0.2967 So, approximately 29.67% of service businesses are successful.
Compare the success rates and conclude Comparing the success rates: S F ≈ 0.3808 S S ≈ 0.2967 Since S_S"> S F > S S , a new food business is more likely to be successful than a new service business.
Final Answer Based on the provided data, it is more likely for a new food business to be successful than a new service business.
Examples
Understanding business success rates can help entrepreneurs make informed decisions. For example, if Perry knows that food businesses have a higher success rate in his city, he might be more inclined to open a restaurant or bakery. This kind of analysis helps reduce risk and increases the chances of a profitable venture. By comparing the success rates of different business types, Perry can strategically choose a business that aligns with the local market conditions and has a higher probability of thriving.
The calculated success rate for food businesses is approximately 38.08%, while for service businesses, it is about 29.67%. Therefore, a new food business is more likely to succeed than a new service business. Perry should consider pursuing a food business for better odds of success.
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