Answer: The mean for the probability distribution will be 69.25.
Explanation:
Since we given that
[tex]At\ x_1= -500 ,P(x) = 0.076\\[/tex]
[tex]At\ x_2= -250,P(x)= 0.191\\[/tex]
[tex]At\ x_3=0, P(x)= 0.265\\[/tex]
[tex]At\ x_4=250 , P(x)= 0.316\\[/tex]
[tex]At\ x_5=500 , P(x)= 0.152\\[/tex]
As we know the formula for expectation of x i.e. known as mean for the probability distribution,
[tex]E(x)=x\sum_{1}^{5} P(x)[/tex]
So, we apply this formula in our case,
[tex]-500\times 0.076+(-250)\times 0.191+0\times 0.265+250\times 0.316+500\times 0.512=69.25[/tex]
[tex]\mu = 69.25[/tex]
Hence, the mean for the probability distribution will be 69.25.
