Respuesta :
Step-by-step explanation:
According to the Empirical rule:
- 68% of the distribution lie within σ of μ.
- 95% of the distribution lie within 2σ of μ.
- 99.7% of the distribution lie within 3σ of μ.
Given:
μ = 48 mph
σ = 17 mph
(1)
Compute the value within which, 68% of the distribution lie as follows:
[tex]P(x_{1}<X<x_{2})=0.68\\P(\mu-\sigma<X<\mu+\sigma)=0.68\\[/tex]
The limits are:
[tex]\mu-\sigma=48-17=31\\\mu+\sigma=48+17=65[/tex]
Thus, according to the Empirical 68% of the distribution of car speed lie between 31 mph and 65 mph.
(2)
Compute the value within which, 95% of the distribution lie as follows:
[tex]P(x_{1}<X<x_{2})=0.95\\P(\mu-2\sigma<X<\mu+2\sigma)=0.95\\[/tex]
The limits are:
[tex]\mu-2\sigma=48-(2\times17)=14\\\mu+2\sigma=48+(2\times17)=82[/tex]
Thus, according to the Empirical 95% of the distribution of car speed lie between 14 mph and 82 mph.
(3)
Compute the value within which, 99.7% of the distribution lie as follows:
[tex]P(x_{1}<X<x_{2})=0.997\\P(\mu-3\sigma<X<\mu+3\sigma)=0.997\\[/tex]
The limits are:
[tex]\mu-3\sigma=48-(\times17)=-3\approx0\\\mu+3\sigma=48+(3\times17)=99[/tex]
Thus, according to the Empirical 99.7% of the distribution of car speed lie between 0 mph and 99 mph.
