Because μ=E(X? )=θ= 100,σ? =D(X？ )=θ? = 10000
So the random variable Z=(∑i= 1~ 16X? -n×μ)/√σ？ *√n=(X- 1600)/400 approximately obeys N(0, 1).
P { X > 1920 } = P {(X- 1600)/400 >( 1920- 1600)/400 } = P {(X- 1600)/400 > 0.8 }
= 1-P {(X- 1600)/400 < 0.8 } = 1-φ(0.8)= 1-0.788 1 = 0.2 1 19
Extended data:
The life distribution of many electronic products generally obeys exponential distribution. The life distribution of some systems can also be approximated by exponential distribution. It is the most commonly used distribution form in reliability research. Exponential distribution is a special case of gamma distribution and Weibull distribution. When the failure of a product is accidental, its life follows an exponential distribution.
When the shape coefficient in Weibull distribution is equal to 1, the exponential distribution can be regarded as a special distribution, and the failure rate of the exponential distribution is a constant independent of time t, so the distribution function is simple.
Baidu encyclopedia-exponential distribution