It has been reported that 83% of federal government employees use email. If a sample of 200 federal government employees is selected, find the mean, variance, and standard deviation of the number who use email.
To find the mean, variance, and standard deviation of the number of federal government employees who use email, we can follow these steps:
Step 1: Calculate the mean (expected value).
The mean, also known as the expected value, can be calculated using the formula:
mean = (total number of successes) * (probability of success)
In this case, the total number of successes is given as 83% of 200, which is (0.83 * 200) = 166.
So, the mean is 166.
Step 2: Calculate the variance.
The variance measures the spread or dispersion of the data around the mean. It can be calculated using the formula:
variance = (total number of trials) * (probability of success) * (probability of failure)
The probability of success is 83% or 0.83, and the probability of failure is 1 - 0.83 = 0.17.
Substituting these values into the formula, we get:
variance = (200) * (0.83) * (0.17)
variance = 27.88
Step 3: Calculate the standard deviation.
The standard deviation is the square root of the variance and measures the average amount of variation or dispersion from the mean.
To calculate the standard deviation, we take the square root of the variance:
standard deviation = sqrt(variance)
standard deviation ≈ sqrt(27.88)
standard deviation ≈ 5.28
Therefore, the mean is 166, the variance is approximately 27.88, and the standard deviation is approximately 5.28, for the number of federal government employees who use email in a sample of 200.
To find the mean, variance, and standard deviation, given that 83% of federal government employees use email, we can follow these steps:
Step 1: Find the mean:
The mean is calculated using the formula:
Mean = (Total number of employees) x (Percentage of employees using email)
Mean = 200 x 83% = 200 x 0.83 = 166
Therefore, the mean number of federal government employees who use email is 166.
Step 2: Find the variance:
Variance is calculated as the average of the squared differences between each observation and the mean.
Variance = (Total number of employees) x (Percentage of employees using email) x (1 - Percentage of employees using email)
Variance = 200 x 83% x (1 - 83%) = 200 x 0.83 x 0.17 = 28.22
Therefore, the variance of the number of federal government employees who use email is 28.22.
Step 3: Find the standard deviation:
The standard deviation is calculated as the square root of the variance.
Standard Deviation = √(Variance) = √28.22 = 5.31 (approx.)
Therefore, the standard deviation of the number of federal government employees who use email is approximately 5.31.
mean = np
variance = npq
standard deviation = square root of the variance
n = 200
p = .83
q = 1 - p
I'll let you take it from here.