below is sampling distribution :
x1 | x2 | probabilityP(x1,x2) | x̅ | Range: | |
1 | 1 | 0.09 | 1 | 0 | |
1 | 2 | 0.12 | 1.5 | 1 | |
1 | 3 | 0.03 | 2 | 2 | |
1 | 4 | 0.06 | 2.5 | 3 | |
2 | 1 | 0.12 | 1.5 | 1 | |
2 | 2 | 0.16 | 2 | 0 | |
2 | 3 | 0.04 | 2.5 | 1 | |
2 | 4 | 0.08 | 3 | 2 | |
3 | 1 | 0.03 | 2 | 2 | |
3 | 2 | 0.04 | 2.5 | 1 | |
3 | 3 | 0.01 | 3 | 0 | |
3 | 4 | 0.02 | 3.5 | 1 | |
4 | 1 | 0.06 | 2.5 | 3 | |
4 | 2 | 0.08 | 3 | 2 | |
4 | 3 | 0.02 | 3.5 | 1 | |
4 | 4 | 0.04 | 4 | 0 |
1)
xbar | 1 | 1.5 | 2 | 2.5 | 3 | 3.5 | 4 |
p(xbar) | 0.09 | 0.24 | 0.22 | 0.2 | 0.17 | 0.04 | 0.04 |
b)
P(Xbar<=2.5)=0.09+0.24+0.22+0.2 =0.75
c)
R | 0 | 1 | 2 | 3 |
P(R ) | 0.3 | 0.36 | 0.22 | 0.12 |
d)
P(x̅ <=1.5)=P(1,1,1,1)+4*P(1,1,1,2)+6*P(1,1,2,2)+4*P(1,1,1,3)=0.3^4+4*0.3^3*0.4+6*0.3^2*0.4^2+4*0.3^3*0.1= | 0.1485 |
Let X be the number of packages being mailed by a randomly selected customer at a...
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