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## AP®︎/College Statistics

### Course: AP®︎/College Statistics>Unit 4

Lesson 4: Normal distributions and the empirical rule

# Qualitative sense of normal distributions

Discussion of how "normal" a distribution might be. Created by Sal Khan.

## Want to join the conversation?

• isnt option d is a discrete distribution, as dates are discrete values?
• Yes and actually, most likely, b and c are discrete too since salaries usually are counted to the penny.
(However, if you have thousands of dollars as a minimum, the single penny will make almost no difference, so they are almost continuous, while d) is not even close to being continuous, since we're not dealing with timespans of 10000s of years for dollars. Not yet, anyways.)
• What is the empirical rule?
• The empirical rule, or the 68-95-99.7 rule, is a rule where almost every value is between three standard deviations of the mean. Find out more in the next video.
• Wouldn't scenario (c) would likely look similar to (b) in the sense that CEOs of smaller companies (who are more numerous) likely make under 500k but the distribution would be heavily rightward skewed by outliers who make enormous salaries? It seems intuitive that there would be some power law relation between CEOs and their salaries, so the distribution from a sample of any size would probably highly non-normal even if we ignore the gender gap and the possibility of a bimodal distribution.
• Well it says in the description '50 CEOs of major companies', so I guess not.
• I was looking for an introduction to the topic "Normal distributions". Actually, I didn't understand anything from the video. How can you guess by yourself if the distribution goes up or down, I mean It's not even written in the question, so how do you know? Is there any previous video which is an introduction to this topic I might miss it!
• Umm, what is a normal distribution? Didn't see it covered before in this course (or did I miss anything?).
• it is the symmetric bell-shaped curve
• I hope I didn't miss anything in the video, but wouldn't c) and d) be approximate normal distributions? Remember: We are talking about big samples (50 CEOS, 100 pennies) and, according to the Central Limit Theorem, it doesn't matter which distribution a single 'trial' follows, the mean will still approach the normal distribution.
• The CLT describes the behavior of the sampling distribution of the sample mean. This video appears to be talking about the distribution of the original data, not the distribution of the sample mean. Hence, the sample size dose nothing for us.

• Wouldn't the graph be left-skewed since it is more on the left?
• This is a common misconception. Skewed graphs actually mean that the tail is stretched out towards that side, for example, a left skewed graph would have a thin tail towards the left, and most of the points are piled up on the right. There should be a video for this too.