Introduction to Probability · 免费预览
正态分布
钟形曲线、其密度与标准化规则、通过标准尺度读取正态概率，以及正态分布为何成为普遍的极限。
1. The standard Normal and its family
The standard Normal and its family
2. The empirical rule and quantiles
The empirical rule and quantiles
3. Symmetry tricks and normal approximations
Symmetry tricks and normal approximations
4. Standardizing correctly
X is Normal with mean 50 and standard deviation 5. What is P(X is at most 60)?
5. The empirical band
Battery lifetimes are Normal(300, 50 squared) hours. Roughly what fraction last between 200 and 400 hours?
6. A symmetric tail
For a standard Normal Z, P(Z is at least 1.5) is about what? Use Phi(1.5) = 0.9332. Enter a decimal like 0.067.
7. A percentile built back
The 97.5th percentile of Z is about 1.96. For X Normal(100, 15 squared), the 97.5th percentile is 100 plus 1.96 times 15. Enter that value rounded to one decimal, like 129.4.
8. Manufacturing tolerance
Rods are Normal(10, 0.1 squared) cm. What is P(a rod is between 9.8 and 10.2)? Use the empirical rule and enter a decimal like 0.95.
9. In your own words
In your own words, state the most important definition, theorem or method of this lesson and explain what it says.