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Slides developed by Mine Çetinkaya-Rundel of OpenIntro

Translated from LaTeX to Google Slides by Curry W. Hilton of OpenIntro.

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Continuous

Distributions

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Continuous distributions

  • Below is a histogram of the distribution of heights of US adults.
  • The proportion of data that falls in the shaded bins gives the probability that a randomly sampled US adult is between 180 cm and 185 cm (about 5'11" to 6'1").

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From histograms

to continuous distributions

Since height is a continuous numerical variable, its probability density function is a smooth curve.

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Probabilities from

continuous distributions

Therefore, the probability that a randomly sampled US adult is between 180 cm and 185 cm can also be estimated as the shaded area under the curve.

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By definition...

Since continuous probabilities are estimated as “the area under the curve”, the probability of a person being exactly 180 cm (or any exact value) is defined as 0.

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