How do I Find P ( 2 < X < 7 )? (Stats)
I Got the part A, but don't get how to do part B.
I Got the part A, but don't get how to do part B.
1 Answer
Explanation:
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Thus,
Since
P(2 < X < 7) = sum_(x=3)^6 P(X = x)P(2<X<7)=6∑x=3P(X=x)
= P(X"=3")+P(X"=4")+P(X"=5")+P(X"=6")=P(X=3)+P(X=4)+P(X=5)+P(X=6)
We just need to find these 4 discrete probabilities.
P(X=3) = (e^-6 xx6^3)/(3!) = 0.0892P(X=3)=e−6×633!=0.0892
P(X=4) = (e^-6 xx6^4)/(4!) = 0.1339P(X=4)=e−6×644!=0.1339
P(X=5) = (e^-6 xx6^5)/(5!) = 0.1606P(X=5)=e−6×655!=0.1606
P(X=6) = (e^-6 xx6^6)/(6!) = 0.1606P(X=6)=e−6×666!=0.1606
Then
P(2 < X < 7)P(2<X<7)
= P(X"=3")+P(X"=4")+P(X"=5")+P(X"=6")=P(X=3)+P(X=4)+P(X=5)+P(X=6)
= 0.0892+0.1339+0.1606+0.1606=0.0892+0.1339+0.1606+0.1606
= 0.5443=0.5443
=54.43%=54.43%