A bell-shaped curve where 68% · 95% · 99.7% pile up around the mean
The normal distribution is a bell-shaped curve symmetric about the mean. Know how much data clusters within a few standard deviations, and you can estimate a whole population's mean just from a sample.
The normal distribution is a symmetric curve whose shape is determined by the mean (μ) and standard deviation (σ). Within one standard deviation of the mean, about 68% of the data is always clustered; within two, about 95%; within three, about 99.7% (this is called the empirical rule).
Estimation means guessing the mean of an entire population by examining only a sample (a portion of it). This is expressed as a confidence interval — the sample mean plus or minus a margin of error — and the larger the sample size, the smaller the margin of error, making the estimate more accurate.
Mean μ0
Standard deviation σ1
When you know the population standard deviation σ, the confidence interval that estimates the population mean from the sample mean x̄ is x̄ ± z×(σ/√n). z is a fixed value depending on the confidence level (95%→1.96, 99%→2.58), and the larger n gets, the smaller σ/√n (the standard error) becomes, narrowing the interval.