Let's calculate the required values step-by-step:
1. Calculate the Sample Mean:
- The data for the number of years worked by employees is: [8, 13, 15, 3, 13, 28, 4, 12, 4, 26, 29, 3, 10, 3, 17, 13, 15, 15, 23, 13].
- First, sum all the years worked: [tex]\(8 + 13 + 15 + 3 + 13 + 28 + 4 + 12 + 4 + 26 + 29 + 3 + 10 + 3 + 17 + 13 + 15 + 15 + 23 + 13 = 276\)[/tex].
- Then, divide by the number of employees: [tex]\( \frac{276}{20} = 13.8 \)[/tex].
- Rounding [tex]\(13.8\)[/tex] to the nearest integer gives us [tex]\(14\)[/tex].
2. Calculate the Percentage of Employees who Worked at Least 10 Years:
- Count the employees who worked at least 10 years: [13, 15, 13, 28, 12, 26, 29, 10, 17, 13, 15, 15, 23, 13]. There are 14 employees in this list.
- Calculate the percentage: [tex]\( \frac{14}{20} \times 100 = 70\% \)[/tex].
So, the sample mean for the number of years worked is [tex]\(13\)[/tex], and [tex]\(70\%\)[/tex] of the employees in the sample worked for the company for at least 10 years.
Thus:
The sample mean for the number of years worked is [tex]\( \boxed{13} \)[/tex], and [tex]\( \boxed{70} \% \)[/tex] of the employees in the sample worked for the company for at least 10 years.
