Normal Distribution Empirical Rule (68-95-99.7 Rule)

Lesson

Notes

Notes for Normal Distribution Empirical Rule

Note: For continuous distributions, \(\lt and \le\) are both treated the same

 

Questions

\(1)\) \(P ( x \lt \mu – \sigma)\)

 

\(2)\) \(P ( x \le \mu – \sigma)\)

 

\(3)\) \(P ( x \gt \mu – 2\sigma)\)

 

\(4)\) \(P ( \mu – \sigma \lt x \lt \mu + \sigma)\)

 

\(5)\) \(P ( \mu – 2\sigma \lt x \lt \mu – \sigma)\)

 

\(6)\) \(P ( \mu – 2\sigma \lt x \lt \mu + 2\sigma)\)

 

\(7)\) \(P ( \mu – 3\sigma \lt x \lt \mu + 3\sigma)\)

 

\(8)\) \(P ( \mu \lt x \lt \mu + 2\sigma)\)

 

\(9)\) \(P ( \mu \lt x \lt \mu + 3\sigma)\)

 

\(10)\) \(P ( \mu – 3\sigma \lt x \lt \mu )\)

 

Challenge Problem

\(11)\) For a normal distribution with mean=1 and standard deviation=1, what percent of the data is less than 0?

 

See Related Pages\(\)

\(\bullet\text{ Statistics Homepage}\)
\(\,\,\,\,\,\,\,\,\text{All the Best Topics…}\)
\(\bullet\text{ Normal Distribution Z-score}\)
\(\,\,\,\,\,\,\,\,z=\displaystyle\frac{\text{value}-\text{mean}}{\text{standard deviation}}\)
\(\bullet\text{ Binomial Distribution}\)
\(\,\,\,\,\,\,\,\,p(r)={}_{n}C_{r}(p)^r(1-p)^{n-r}…\)
\(\bullet\text{ Geometric Distribution}\)
\(\,\,\,\,\,\,\,\,P(X=n)=p(1-p)^{n-1}…\)

 

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