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Chapter 8: Q. 8.24 (page 392)

ItXis a Poisson random variable with a mean100, thenPX>120is approximately

(a).02,

(b).5or

(c).3?

Short Answer

Expert verified

Then,PX>120is approximately (a).02.

Step by step solution

01

Given Information.

Xis a Poisson random variable with a mean100.

02

Explanation.

Suppose thatX1,鈥�,X100is independent and equally distributed with the distributionPois(1). Therefore

X=鈭�iXi~Pois(100)

Using the Central Limit Theorem, we can approximate that

X~ANnEX1,VarX1=AN(100,1)

Therefore, we have an approximation

P(X>120)=PX-nEX1VarX1>120-nEX1VarX1

=PX-nEX1VarX1>20鈮�1-桅(20)=0.02

so the right answer is(a).

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