Head First Statistics by Dawn Griffiths

Author:Dawn Griffiths [Dawn Griffiths]
Language: eng
Format: epub, mobi, pdf
Tags: MATHEMATICS / Probability & Statistics / General
ISBN: 9780596558727
Publisher: O'Reilly Media
Published: 2009-06-29T16:00:00+00:00

Can you see where the problem lies?

When we take integers from a discrete probability distribution and translate them onto a continuous scale, we don’t just look at those precise values in isolation. Instead, we look at the range of numbers that round to each of the values.

Let’s take the discrete value 6 as an example. When we translate the number 6 to a continuous scale, we need to consider all of the numbers that round to it—in other words, the entire range of numbers from 5.5 to 6.5.

So how does this apply to our probability problem?

When we tried using the normal distribution to approximate the probability of getting fewer than 6 questions correct, we didn’t look at how the discrete value 6 translates onto a continuous scale. The discrete value 6 actually covers a range from 5.5 to 6.5, so instead of using the normal distribution to find P(X < 6), we should have tried calculating P(X < 5.5) instead.

This adjustment is called a continuity correction. A continuity correction is the small adjustment that needs to be made when you translate discrete values onto a continuous scale.

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