Question

days off number of employees 0 to 5 3 6 to 10 5 11 to 15 8 16 to 20 7 more than 20 2 company x randomly surveyed 25 employees about the number of days they took off last year. the table shows the results of the survey. if the survey results are representative of all 225 employees at company x, what is a reasonable estimate of the number of employees who took off 16 or more days last year?

Explanation:

Step1: Calculate the number of employees who took off 16 or more days in the survey

In the survey, the number of employees who took off 16 - 20 days is 7 and more than 20 days is 2. So the total number of employees who took off 16 or more days in the survey is \(7 + 2=9\).

Step2: Set up a proportion

Let \(x\) be the number of employees who took off 16 or more days in the whole company. We know that the proportion of employees who took off 16 or more days in the survey to the total number of surveyed employees is equal to the proportion of employees who took off 16 or more days in the whole company to the total number of employees in the company.
The proportion is \(\frac{9}{25}=\frac{x}{225}\).

Step3: Solve the proportion for \(x\)

Cross - multiply: \(25x=9\times225\).
First, calculate \(9\times225 = 2025\). Then \(x=\frac{2025}{25}=81\).

Answer:

81