In Exercises 37–44, answer the given questions, which are rela...

Question

In Exercises 37–44, answer the given questions, which are related to percentages.

Checking Job Applicants In a study conducted by the Society for Human Resource Management, 347 human resource professionals were surveyed. Of those surveyed, 73% said that their companies conduct criminal background checks on all job applicants.

a. What is the exact value that is 73% of the 347 survey subjects?

b. Could the result from part (a) be the actual number of survey subjects who said that their companies conduct criminal background checks on all job applicants? Why or why not?

Accepted Answer

All right, hello, everyone. So, this question says, in a survey conducted by the National College Admissions Council, 412 college admission officers were surveyed. Of those surveyed, 68% said that their institutions require standardized test scores for all candidates. Part A is asking what is the exact value that is 68% of the 412 survey subjects. Part B is asking, could the result from the preceding part be the actual number of survey respondents who stated that their institutions require standardized test scores for all candidates? Why or why not? And here we have 4 different answer choices stating not only the exact value. Of the 68% for Part A, but also a yes or no, as well as a justification for the second part of the question. All right, so first, to understand the answer to Part A, you first have to recall. The formula of a percentage, right? Recall a percentage is a part of a whole. So in this particular context, we don't. We don't have the exact number of admissions officers that responded that standardized test scores are required for their institutions, right? But we do have the actual percentage which is ultimately going to help us. So quality percentage is equal to. The part of interest divided by the total number. Multiplied by 100. Now When given a percentage. What you could do is convert that percentage back into a decimal. Because in the original calculation of a percentage. The part divided by the total gives you a decimal which you then multiply by 100. So when you take your 60%, for example, or rather 68%. If you take your 68%, and you divide that by 100, you get the original decimal. Which in this case would be 0.68. And so when you're trying to find the exact number. For example, if. You're trying to find 68% of 412. What you do is multiply the total. By the percentage as a decimal. So here, I will multiply my total of 412 by my 68%, but as a decimal. So that expression comes out to 0.68, multiplied by 412, which gives me 280.16. So 280.16 is my exact answer for part A of this question. And so part B is about taking the number that you just calculated. And applying it to the context of. Your survey right of your data in a way that makes sense. So here, right. The question is asking, can the. Number 10 280.16. Be reported as the total number of respondents. That answered yes to standardized exams. Well, it's important to take this number in context, right? Because 280.16 is not an integer, it's not a whole number. But in this case, 280.16 is supposed to represent the number of people. That responded to the survey. Now, in this context. You cannot include. A fraction of a person as a respondent, right? So in this context, when you're applying this number to a sample size, you have to round to the nearest whole number. So in this case, 280.16 would instead be rounded to 280 people. Because once again, you cannot use a fraction of a person for a. Sample size. So going back to the original answer choices. The correct answer would be option D. So for part A, the answer is 280.16. And for Part B, you would say no, because the actual number must be a whole number, so it would be rounded to 280. And there you have it. So with that being said, thank you so very much for watching, and I hope you found this helpful.

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Key Concepts

Percentage Calculation

Rounding and Exact Values

Survey Interpretation

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