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Problem-Solving and Data Analysis / Inference from sample statistics and margin of error Difficulty: Easy

Scott selected $20$ employees at random from all $400$ employees at a company. He found that $16$ of the employees in this sample are enrolled in exactly three professional development courses this year. Based on Scott’s findings, which of the following is the best estimate of the number of employees at the company who are enrolled in exactly three professional development courses this year?

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Explanation

Choice B is correct. It’s given that from the sample of $20$ employees at the company, $16$ of the employees are enrolled in exactly three professional development courses this year. Since $left parenthesis StartFraction 16 Over 20 EndFraction right parenthesis$ is equal to $0.80$ , or $StartFraction 80 Over 100 EndFraction$ , it follows that $80 percent sign$ of the employees in the sample are enrolled in exactly three professional development courses this year. Therefore, the best estimate for the percentage of employees at the company who are enrolled in exactly three professional development courses this year is $80 percent sign$ . It’s given that there are a total of $400$ employees at the company. Therefore, the best estimate of the number of employees at the company who are enrolled in exactly three professional development courses this year is $left parenthesis StartFraction 80 Over 100 EndFraction right parenthesis left parenthesis 400 right parenthesis$ , or $320$ .

Choice A is incorrect. This is the number of employees from the sample who aren't enrolled in exactly three professional development courses this year.

Choice C is incorrect. This is the number of employees who weren't selected for the sample.

Choice D is incorrect and may result from conceptual or calculation errors.