Learn how to use the empirical rule (or 689599.7 rule) to estimate probabilities for normal distributions in statistics. From Ramanujan to calculus cocreator Gottfried Leibniz, many of the world's best and brightest mathematical minds have belonged to autodidacts. And, thanks to the Internet, it's easier than ever to follow in their footsteps (or just finish your homework or study for that next big test). With this installment from Internet pedagogical superstar Salman Khan's series of free math tutorials, you'll learn how to estimate probabilities for a bell distribution.
 Hot
 Latest

How To: Remember "greater than" & "less than" symbols

How To: Use ">" (greater than) and "<" (less than) symbols

How To: Calculate Faster Than a Calculator

How To: Find the Percent Given Two Numbers

How To: Identify characteristics of a sample during a survey

How To: Find the 100th term in a sequence

How To: Find the formula of a piecewise function given a graph

How To: Find and sketch the domain of a multivariable function

How To: Determine the eigenvalues of a 3x3 matrix

How To: Divide fractions by multiplying by the reciprocal

How To: Find a number given Its percent

How To: Find a slope of a straight line with: Ax + By + C = 0

How To: Find extra points for a parabola (quadractic equation)

How To: Calculate the area of a parallelogram

How To: Find the area of a triangle when given 2 sides & angle

How To: Find a missing side of a triangle, similar to another

How To: Find the area of a circle when you know the diameter

How To: Find the Radius of a Circle from Arc Length

How To: Calculate the height and volume of a pyramid

How To: Find a missing angle outside of a triangle

How To: Remember "greater than" & "less than" symbols

How To: Use ">" (greater than) and "<" (less than) symbols

How To: Calculate Faster Than a Calculator

How To: Find the Percent Given Two Numbers

How To: Identify characteristics of a sample during a survey

How To: Find the 100th term in a sequence

How To: Find the formula of a piecewise function given a graph

How To: Find and sketch the domain of a multivariable function

How To: Determine the eigenvalues of a 3x3 matrix

How To: Divide fractions by multiplying by the reciprocal

How To: Find a number given Its percent

How To: Find a slope of a straight line with: Ax + By + C = 0

How To: Find extra points for a parabola (quadractic equation)

How To: Calculate the area of a parallelogram

How To: Find the area of a triangle when given 2 sides & angle

How To: Find a missing side of a triangle, similar to another

How To: Find the area of a circle when you know the diameter

How To: Find the Radius of a Circle from Arc Length

How To: Calculate the height and volume of a pyramid

How To: Find a missing angle outside of a triangle
2 Comments
what percentage of women have shoe sizes greater than 11.33 if the mean is 8.27 and the deviation is 1.53?
Since the larger shoe size is two standard deviations above the mean, one expects it is exceeded by about 2.5% of the shoe sizes sampled, if shoe sizes follow the normal distribution and the sample is large enough. (The 0.68, 0.95, 0.997 in the rule are the the areas within 1, 2, or 3 standard deviations of the mean. In each case, onehalf the area located farther from the mean is in the high tail, on the right side of a bell curve graph. So 100%  95% = 5%, of which half, or 2.5%, is in the high tail.) In general, however, the bell curve works best at predicting percentages that score in ranges close to the mean, and becomes less accurate for unusually high or low scores. Two standard deviations is as far as one should extrapolate a bell curve with most social science variables. It is also possible to reify the bell curve as IQ tests do: The way the tests are scored forces them to fit a bell curve, albeit with reproducible results. But from this we can't conclude that human intelligence, the thing IQ tests are supposed to measure, is normally distributed, or even linear for that matter. In fact there's good reason to think that intelligence isn't additive like linear functions are. The "smartest" people may enjoy only a slight edge in raw computational brain power over their "dumbest" peers; intellectual tasks being of a nature where a very few extra neural connections of the right kind have a big effect on results.
Share Your Thoughts