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A person aiming at a target receives 10 points if their shot is within 1 inch of the target, 5 points if it is between 1 and 3 inches of the target, and 3 points if it is between 3 and 5 inches of the target. In any other case, they will receive 0 points. Find the expected number of points scored if the distance from their shot to the target is a uniformly distributed value between 0 and 10.

Respuesta :

Answer:

standard deviation is 2.886 [expected points]

Step-by-step explanation:

Let x is number of points scored so that given target uniformly dstributed between 0 and 10

clearly X uniform(0,10)

mean is defined as [tex]E(x) = \frac{a+b}{2}[/tex]

                                       [tex]\frac{0+10}{2} = 5[/tex]

we know that variance is given as [tex]\frac{(b-a)^2}{12}[/tex]

[tex]V(x) = \frac{(b-a)^2}{12}[/tex]

       [tex]\frac{(10-0)^2}{12}[/tex]

       = 8.333

therefore standard deviation is [tex]\sqrt{V(x)} = \sqrt{8.333}[/tex]

standard deviation is 2.886 [expected points]

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