Answer:
24.53
Step-by-step explanation:
We need to define our data, that is
w -> x
0.04->340
0.11->460
0.47->540
0.38->650
We can obtain our mean,
[tex]\bar{x} = \frac{\sum\limit_{i=1}^n x_iw_i}{\sum\limit_{i=1}^n w_i}[/tex]
[tex]\bar{x} = \frac{(0.04*340)+(0.11*460)+(0.47*540)+(650*0.38)}{1}[/tex]
[tex]\bar{x} = 570.7070[/tex]
To find the SE we need the Variance,
[tex]V(x) = E(x^2) - E(x)^2[/tex]
Make [tex]E(x)=\bar{x}[/tex], then
[tex]E(x^2)=\frac{(0.04*340^2)+(0.11*460^2)+(0.47*540^2)+(650^2*0.38)}{1}[/tex]
[tex]E(x^2) = 325502[/tex]
[tex]V(x) = 325502 - 570^2[/tex]
[tex]V(x) = 602[/tex]
[tex]SE = \sqrt{V(x)} = \sqrt{602} = 24.53[/tex]
