1. **Problem Statement:** We are given that 83% of federal government employees use e-mail. From a sample of 210 employees, we need to find the mean, variance, and standard deviation of the number who use e-mail. 2. **Relevant Formulas for Binomial Distribution:** - Mean (expected value): $$\mu = n \times p$$ - Variance: $$\sigma^2 = n \times p \times (1-p)$$ - Standard deviation: $$\sigma = \sqrt{\sigma^2}$$ 3. **Given Values:** - Number of trials (employees): $$n = 210$$ - Probability of success (using e-mail): $$p = 0.83$$ 4. **Calculate the Mean:** $$\mu = 210 \times 0.83 = 174.3$$ 5. **Calculate the Variance:** $$\sigma^2 = 210 \times 0.83 \times (1 - 0.83) = 210 \times 0.83 \times 0.17$$ $$\sigma^2 = 29.601$$ 6. **Calculate the Standard Deviation:** $$\sigma = \sqrt{29.601} \approx 5.441$$ **Final answers:** - Mean: 174.3 - Variance: 29.601 - Standard deviation: 5.441 These values describe the expected number of employees using e-mail and the variability around that expectation in the sample of 210 employees.