Chebyshev's Theorem

[Buse Özden]

Hello everybody.

There is a part that I do not understand at the document Professor recommended us to read which is called "The Empirical Rule and Chebyshev's Theorem".

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Example 2.5.4

4. On at most 25% of the weekday mornings last year, the number of vehicles passing through the intersection from 8:00 a.m. to 10:00 a.m. was either less than 675 or greater than 775.

6.On at most 25% of the weekday mornings last year the number of vehicles passing through the intersection from 8:00 a.m. to 10:00 a.m. was less than 675.

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The 4th statement is correct. However, I do not understand why it should be either less than 675 or greater than 775, and not both. Why is that?

Since I do not understand the 4th statement I do not understand the 6th either. According to the explanation, the 6th statement must be correct. If the 4th statement is correct also, why the 6th suggest that 25% of the vesicles must be less than 675? Do we not have 2 possibilities according to the 4th statement —either less than 675 and greater than 775?

Thanks in advance. Have a great week. 

Buse

[Dr. Andrés Aravena]

Anybody?

This is a good question. I hope to see your opinions here.