It has been reported that 86% of federal government employees use email. If a sample of 175 federal government employees is selected, find the mean, varience, and standard deviation of the number who use email.
mean = np
variance = npq
Note: q = 1 - p
standard deviation = square root of the variance
I'll get you started and let you finish the calculations:
mean = 175 * .86 = ?
variance = 175 * .86 * .14 = ?
Note: * means to multiply
I hope this will help.
To find the mean, variance, and standard deviation of the number of federal government employees who use email, we first need to identify the relevant formulas and gather the necessary data.
Let's start with the mean:
Mean (μ) = (Sum of all data points) / (Number of data points)
For this problem, the mean represents the average number of federal government employees who use email.
Given that 86% of federal government employees use email, we can calculate the mean as follows:
Mean (μ) = 175 * 0.86
Therefore, the mean is 150.5 federal government employees who use email.
Next, let's move on to the variance:
Variance (σ^2) = (Sum of squared deviations from the mean) / (Number of data points)
This formula measures how spread out the data is. We will need to calculate the squared deviations from the mean.
To find the squared deviation for each data point, subtract the mean from each data point, square the result, and sum up all the squared deviations. Then divide by the number of data points:
Variance (σ^2) = Σ (x - μ)^2 / n
In this case, we have a binomial distribution because we are dealing with a yes/no scenario: whether a federal employee uses email or not. The variance of a binomial distribution can be calculated using the formula:
Variance (σ^2) = n * p * (1 - p)
Where n is the number of trials (175) and p is the probability of success (86%).
Plugging in the values, we get:
Variance (σ^2) = 175 * 0.86 * (1 - 0.86)
Therefore, the variance is 21.19.
Finally, let's calculate the standard deviation:
Standard Deviation (σ) = √Variance
Using the variance we found in the previous step:
Standard Deviation (σ) = √21.19
Therefore, the standard deviation is approximately 4.60.
To summarize:
- Mean (μ) = 150.5 federal government employees who use email
- Variance (σ^2) = 21.19
- Standard Deviation (σ) = approximately 4.60 federal government employees.