The two tables below show the success rates of several groups of businesses in a certain city. The first shows the number of businesses of several types started in Sharon’s city over the course of two years, and the number of those businesses which did not succeed and were forced to shut down within two years of opening. The second deals with separate records of successful new businesses, showing how much profit those new businesses turned over two years. Businesses on the boundary lines fall in the lower category.TypeFoodRetailFinancialServiceOpened3,1932,2801,8985,045Closed1,9771,6261,4433,548 Up to $25k$25-50k$50-75k$75-100kOver $100kFood945623601258114Retail81354834718863Financial3162441958651Service979739432174124Using the tables as experimental data, determine which of the following situations have a probability of at least 15.00%.I. a food establishment succeeding and earning $50,000 or moreII. a service establishment succeeding and earning between $25,000 and $75,000III. a retail establishment succeeding and earning no more than $50,000
For each situation, multiply the chance that the business succeeds by the share of successful businesses in the stated profit range. For I, the estimate is (3,193 − 1,977)/3,193 × (601 + 258 + 114)/2,541 ≈ 14.6%, below 15%. For II, it is (5,045 − 3,548)/5,045 × (739 + 432)/2,448 ≈ 14.2%, also below 15%. For III, it is (2,280 − 1,626)/2,280 × (813 + 548)/1,959 ≈ 19.9%, so only III qualifies: choice D, “III only.”
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