Answer:
To figure out the mean, we will use the formula below
[tex]\sum_{n\mathop{=}0}^4x.P(x)[/tex]
when x=0
[tex]x.P(x)=0\times1.30=0[/tex]
When x=1
[tex]x.P(x)=1\times0.40=0.40[/tex]
when x=2
[tex]x.P(x)=2\times0.20=0.40[/tex]
When x=3
[tex]x.P(x)=3\times0.06=0.18[/tex]
When x= 4
[tex]x.P(x)=4\times0.04=0.16[/tex]
Hence,
The mean of the distribution will be
[tex]\sum_{n\mathop{=}0}^4x.P(x)=0+0.40+0.40+0.18+0.16=1.14[/tex]
Hence,
The mean is
[tex]\Rightarrow1.14[/tex]
To figure out the standar deviation, we will use the formula below
[tex]\sigma^2=\sum_{n\mathop{=}1}^4(x-\mu)^2P(x)[/tex]
when x=0
[tex](0-1.14)^2\times0.30=0.38988[/tex]
when x= 1
[tex](1-1.14)^2\times0.40=0.00784[/tex]
when x=2
[tex](2-1.14)^2\times0.20=0.14792[/tex]
When x=3
[tex](3-1.14)^2\times0.06=0.20758[/tex]
When x=4
[tex](4-1.14)^2\times0.04=0.327184[/tex]
Add them up and find the square root
[tex]\begin{gathered} \sigma^2=0.38988+0.00784+0.14792+0.20758+0.327184 \\ \sigma^2=1.080404 \\ \sigma=\sqrt{1.080404} \\ \sigma=1.04 \end{gathered}[/tex]
Hence,
The mean = 1.14 and the standard deviation is =1.04
OPTION A is the right answer
