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The number of trees in one acre has a Poisson distribution
Chapter 5, Problem 17E(choose chapter or problem)
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.
Questions & Answers
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