IF Y~B(11, 0.3), find (|Y-5| >= 3)(adsbygoogle = window.adsbygoogle || []).push({});

I got the answer(0.3170) but i don't understand the logic behind this part where i am confused.

can someone explain the working(second working) where i somehow got it blindly correct?

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my working at first:

|Y-5| >= 3

Y >= 8

Y <=2

so P( 2 >= Y >= 8)

P(Y=8) = 0.9994

1 - 0.9994 = 0.0006

P(Y=2) = 0.3127

so P( 2 >= Y >= 8) = 0.3133

However this answer is wrong

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My second working:

my working at first:

|Y-5| >= 3

Y >= 8

Y <=2

so P( 2 >= Y >= 8)

P(Y=7) = 0.9957

1 - 0.9957 = 0.0043

P(Y=2) = 0.3127

so P( 2 >= Y >= 8) = 0.3170

This is the correct working but i don't understand why Y is = 7....

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# Binomial Distribution Help

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