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Normal Distribution Curve, a la Shmoop All Gene “the Green Bean” wants is to

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be normal.

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As you might imagine, however, someone with the nickname Green Bean might have some trouble

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in the… normal department. Of course, Gene may be a perfectly normal

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human being…

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…but we’re more interested in Normal in the mathematical sense.

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The normal curve looks like this. It’s the bell shaped graph that results when statisticians

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plot data with a… normal distribution. Basically, the total area under the curve

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equals… one.

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This area is divided up into standard deviations… the areas to the left and right of the middle

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of the curve…

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…and it also happens to be the average of the data.

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Take male height for example.

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The average height of an adult male is seventy inches, or five feet ten inches, with a standard

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deviation of four inches.

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That means that sixty-eight point two percent of all males are within four inches of five

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foot ten. These guys are considered “normal.”

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Unfortunately for Gene, at six foot five, he falls two deviations away from the average.

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The second deviation from either side of the midpoint makes up twenty seven point three

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percent of the area under the curve.

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In Gene’s case, he falls into the twenty seven point three percent of the population

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who is either shorter than five six or taller than six two.

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So he has to shop at one of these. At least Gene still falls into the ninety

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five point five percent of the population within two standard deviations of the average.

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But what about that other four point five percent? Who are those guys?

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Anyone shorter than five two or taller than six six will land three standard deviations

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from the average.

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These guys make up four point two percent of the population.

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That means that ninety-nine point eight percent of men stand within three standard deviations

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of five feet ten inches tall. So Gene may not fall within one deviation

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for height… but what about his other features?

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Maybe nose length? Whoa, nope.

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How about hair color? Sorry, don’t think Gene will be with the majority on that one

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either.

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Hey, wait a minute. With that big head of his he’s got to have a decent IQ, right?

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Let’s see where the Green Bean falls.

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The average IQ score is one hundred.

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The standard deviation is fifteen points, so does Gene fall within one standard deviation?

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Sweet! Gene, with his barely above average IQ…

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…can join sixty eight point two percent of the population within one standard deviation

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of the average.

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Congratulations, average pants!

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