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 16 or more days off in the sample

In the sample of 25 employees, the number of employees who took 16 or more days off is \(7 + 2=9\)

Step2: Set up a proportion to estimate the number in the whole company

Let \(x\) be the number of employees in the whole company (\(N = 225\)) who took 16 or more days off.
We use the proportion \(\frac{\text{Sample - 16 or more}}{\text{Sample - total}}=\frac{\text{Population - 16 or more}}{\text{Population - total}}\)
So \(\frac{9}{25}=\frac{x}{225}\)

Step3: Solve the proportion for \(x\)

Cross - multiply: \(25x=9\times225\)
\(x=\frac{9\times225}{25}\)
Since \(225\div25 = 9\), then \(x=9\times9\)
\(x = 81\)

Answer:

81