Knowing the population standard deviation, a 95% confidence interval infers that the population mean is between 0 and 100% is within ±1.96 standard deviations of the sample mean is within ±1.96 standard errors of the sample mean is too large

within ±1.96 standard deviations of the sample mean

Step-by-step explanation:

A 95% confidence interval is found using the formula C = 1 - α, and some other stuff, but let's focus on that for now. Using the formula:

.95 = 1 - α

α = .05

If α = .05, that means a 2-sided confidence interval would be found using the sample mean and the Z-score Z(subscript α/2), or Z.₀₂₅ because α AKA .05 divided by 2 = .025. From there, you take this either to your calculator or a Z-table (or perhaps you have a chart that lists the common CI values), and see that for the area to be .025 beneath a standard normal curve, your Z value is ±1.96 ("plus or minus" because we're considering a 2-sided confidence interval).

2.83941151 would be the answer you're looking for! : )

a is the correct