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).
