Question - normal distribution

[happyman]

For a normal distribution, what approximate % of the observations fall within +_3 standard deviation of the mean?
a. 66%
b. 95%
c. 99%

Dap an: c

Giai thich giúp tớ tại sao ra c nhỉ. Many thanks

 

[cinderelly]

Ðề: Question - normal distribution

Quy về Z ~ N(0,1) và P(-3<=Z<=3) = 99.7% cũng duoc gọi là xấp xỉ 99% roi,

 

[hanvinh]

Ðề: Question - normal distribution

Câu này có trong lý thuyết rùi, bạn đọc kỹ hơn lý thuyết nhé. Cái này bạn tra Z-table, xem với giá trị bằng 3 là bao nhiêu %.

Có mấy giá trị cộc móc như sau:
- 68% thuộc range: Mean +- 1 standard deviation
- 95% thuộc range: Mean +- 1.96 standard deviation
- 99% thuộc range: Mean +- 2.58 standard deviation

Ở đây chắc làm tròn số nên nó bằng 3

 

[kingeric]

Ðề: Question - normal distribution

Chắc bạn đang lăn tăn kết quả theo đáp án cho với cách tính của công thức Chebyshev phải không . Bạn tham khảo thêm nhé:

The Empirical Rule applies solely to the NORMAL distribution, while Chebyshev's Theorem (Chebyshev's Inequality, Tchebysheff's Inequality, Bienaymé-Chebyshev Inequality) deals with ALL (well, rather, REAL-WORLD) distributions. The Empirical Rule is stronger than Chebyshev's Inequality, but applies to fewer cases.

The Empirical Rule:
- Applies to normal distributions.
- About 68% of the values lie within one standard deviation of the mean.
- About 95% of the values lie within two standard deviations of the mean.
- About 99.7% of the values lie within three standard deviations of the mean.
- For more precise values or values for another interval, use a normalcdf function on a calculator or integrate e^(-(x - mu)^2/(2*(sigma^2))) / (sigma*sqrt(2*pi)) along the desired interval (where mu is the population mean and sigma is the population standard deviation).

Chebyshev's Theorem/Inequality:
- Applies to all (real-world) distributions.
- No more than 1/(k^2) of the values are more than k standard deviations away from the mean. This yields the following in comparison to the Empirical Rule:
- No more than [all] of the values are more than 1 standard deviation away from the mean.
- No more than 1/4 of the values are more than 2 standard deviations away from the mean.
- No more than 1/9 of the values are more than 3 standard deviations away from the mean.
- This is weaker than the Empirical Rule for the case of the normal distribution, but can be applied to all (real-world) distributions. For example, for a normal distribution, Chebyshev's Inequality states that at most 1/4 of the values are beyond 2 standard deviations from the mean, which means that at least 75% are within 2 standard deviations of the mean. The Empirical Rule makes the much stronger statement that about 95% of the values are within 2 standard deviations of the mean. However, for a distribution that has significant skew or other attributes that do not match the normal distribution, one can use Chebyshev's Inequality, but not the Empirical Rule.
- Chebyshev's Inequality is a "fall-back" for distributions that cannot be modeled by approximations with more specific rules and provisions, such as the Empirical Rule.

Read more: http://wiki.answers.com/Q/What_are_...al_Rule_and_Chebyshev's_Theorem#ixzz1nZMLWJw3