An more useful thing to remember is Shah's approximation, which estimates the area under the standard normal curve from 0 to a point 𝑧 on the x axis as follows

An more useful thing to remember is Shah's approximation, which estimates the area under the standard normal curve from 0 to a point 𝑧 on the x axis as follows: • 𝑧(4.4 – 𝑧)/10 when 0 ≤ 𝑧 ≤ 2.2 • 0.49 when 2.2 < 𝑧 < 2.6 • 0.50 when 2.6 ≤ 𝑧 Shah's approximation is accurate to within roughly ±½%. Examples: - The area under the standard normal curve within 1 standard deviation of zero is approximately 2(1(4.4 – 1))/10 = 0.68. (The factor of 2 is there to get the area on both sides of zero). - The area within 2 standard deviations of zero is approximately 2(2(4.4 – 2))/10 = 0.96. - The area within 3 standard deviations of zero is approximately 1 (because 2.6 ≤ 3). - The probability of sampling from the standard normal distribution and getting a value less than 1.5 deviations above the mean is approximately 0.5 + 1.5(4.4-1.5) = 0.935. (The 0.5 term is there because we need to include the area to the left of 0, and Shah's approximation only counts the area to the right of zero.) Reference: Arvind K. Shah (1985) A Simpler Approximation for Areas under the Standard Normal Curve, The American Statistician, 39:1, 80, DOI: 10.1080/00031305.1985.10479396 (https://twitter.com/jordancurve/status/958026273149915136/photo/2 https://twitter.com/jordancurve/status/958026273149915136/ph...)