Final answer:
The margin of error for a 95% confidence interval with a sample mean of 4,284.42, a population standard deviation of 2,537.36, and a sample size of 44 is approximately 750.94 megabytes.
Step-by-step explanation:
To calculate the margin of error for a 95% confidence interval when the population standard deviation is known, we use the formula for the margin of error associated with a normally distributed population:
Margin of Error = Z * (σ/√n)
Where Z is the Z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.
For a 95% confidence level, the Z-score is typically 1.96. We can now plug in the given values:
σ = 2,537.36
n = 44
The calculation is:
Margin of Error = 1.96 * (2,537.36/√44)
Margin of Error = 1.96 * (383.13)
Margin of Error ≈ 750.94 megabytes
Therefore, we estimate with 95% confidence that the true mean of monthly data usage is within 750.94 megabytes of the sample mean, 4,284.42 megabytes.