Final answer:
The margin of error for a 95% confidence interval for μ with n=56 and σ=4.5 is approximately 1.179, which is found using the z-score for 95% confidence and the formula for margin of error.
Step-by-step explanation:
The margin of error for a 95% confidence interval for μ with n=56 and σ=4.5 is approximately 1.179, which is found using the z-score for 95% confidence and the formula for margin of error.
To find the margin of error for a 95% confidence interval for μ when the sample size is n=56 and the population standard deviation is σ = 4.5, we need to use the formula for the margin of error in a normal distribution which is E = Z * (σ/√n), where Z is the z-score corresponding to the 95% confidence level.
For a 95% confidence interval, the z-score is commonly 1.96. Applying the formula, we get E = 1.96 * (4.5/√56), which we need to calculate.
First, find the standard error by dividing the standard deviation by the square root of the sample size:
Standard Error (SE) = 4.5 / √56 = 4.5 / 7.4833 = 0.6015
Then, calculate the margin of error:
Margin of Error (E) = 1.96 * SE = 1.96 * 0.6015 = 1.179
Therefore, the margin of error for a 95% confidence interval for μ is approximately 1.179.