Respuesta :
Answer:
a) [tex] E(X) = \frac{a+b}{2}=\frac{670+750}{2}= 710[/tex]
The variance is given by:
[tex] Var(X) =\frac{(b-a)^2}{12}= \frac{(750-670)^2}{12}= 5333.3333[/tex]
And the deviation is just the square root of the variance and we got:
[tex] Sd(X) = \sqrt{5333.333}= 23.09[/tex]
b) [tex] P(X<730)[/tex]
And for this case we can use the cumulative distribution given by:
[tex] F(X) = \frac{x-a}{b-a} , a \leq x \leq b[/tex]
And replacing we got:
[tex] P(X<730)= F(730) = \frac{730-670}{750-670}=0.75[/tex]
Step-by-step explanation:
For this case we assume that X is our random variable and we know that the distribution for X is given by:
[tex] X \sim Unif(a=670, b = 750)[/tex]
Part a
For this case the expected value is given by:
[tex] E(X) = \frac{a+b}{2}=\frac{670+750}{2}= 710[/tex]
The variance is given by:
[tex] Var(X) =\frac{(b-a)^2}{12}= \frac{(750-670)^2}{12}= 5333.3333[/tex]
And the deviation is just the square root of the variance and we got:
[tex] Sd(X) = \sqrt{5333.333}= 23.09[/tex]
Part b
For this case we want to find this probability:
[tex] P(X<730)[/tex]
And for this case we can use the cumulative distribution given by:
[tex] F(X) = \frac{x-a}{b-a} , a \leq x \leq b[/tex]
And replacing we got:
[tex] P(X<730)= F(730) = \frac{730-670}{750-670}=0.75[/tex]
