How do I Find P ( 2 < X < 7 )? (Stats)

I Got the part A, but don't get how to do part B.enter image source here

1 Answer
May 16, 2018

P(2<X<7)=54.43%.

Explanation:

The picture is a bit blurry, but it appears as though X is the number of calls over a 1.5 minute interval. Thus, X ~ Poisson(λ) where λ=1.5×4=6.

Thus, P(X=x) =e6×6xx!

Since X is discrete, we know

P(2<X<7)=6x=3P(X=x)

=P(X=3)+P(X=4)+P(X=5)+P(X=6)

We just need to find these 4 discrete probabilities.

P(X=3)=e6×633!=0.0892

P(X=4)=e6×644!=0.1339

P(X=5)=e6×655!=0.1606

P(X=6)=e6×666!=0.1606

Then

P(2<X<7)

=P(X=3)+P(X=4)+P(X=5)+P(X=6)

=0.0892+0.1339+0.1606+0.1606

=0.5443
=54.43%