The number of trees in one acre has a Poisson distribution

Chapter 5, Problem 17E

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QUESTION:

The number of trees in one acre has a Poisson distribution with mean 60. Assuming independence, compute \(P(5950 \le X \le 6100)\), approximately, where X is the number of trees in 100 acres.

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QUESTION:

The number of trees in one acre has a Poisson distribution with mean 60. Assuming independence, compute \(P(5950 \le X \le 6100)\), approximately, where X is the number of trees in 100 acres.

ANSWER:

Step 1 of 2

Let  be the number of trees in each acre.

Then each

Therefore,

The probability mass function of random variable X is as follows:

 

By using the central limit theorem, then has approximately a normal distribution with

       And      

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