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Statistics / Applied Statistics and Probability for Engineers 6 / Chapter 3.9 / Problem 209SE

Applied Statistics and Probability for Engineers | 6th Edition | ISBN: 9781118539712 | Authors: Douglas C. Montgomery, George C. Runger

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Saguaro cacti are large cacti indigenous to the

Chapter 3, Problem 209SE

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QUESTION:

Problem 209SE

Saguaro cacti are large cacti indigenous to the southwestern United States and Mexico. Assume that the number of saguaro cacti in a region follows a Poisson distribution with a mean of 280 per square kilometer. Determine the following:

(a) Mean number of cacti per 10,000 square meters.

(b) Probability of no cacti in 10,000 square meters.

(c) Area of a region such that the probability of at least two cacti in the region is 0.9.

Questions & Answers

QUESTION:

Problem 209SE

Saguaro cacti are large cacti indigenous to the southwestern United States and Mexico. Assume that the number of saguaro cacti in a region follows a Poisson distribution with a mean of 280 per square kilometer. Determine the following:

(a) Mean number of cacti per 10,000 square meters.

(b) Probability of no cacti in 10,000 square meters.

(c) Area of a region such that the probability of at least two cacti in the region is 0.9.

ANSWER:

Solution:

Step 1 of 3:

The number of saguaro cacti in a region follows a poisson distribution with a mean of 280 per square kilometer.

We have to find the mean number of cacti per 10,000 square meters.
We have to find the probability of no cacti in 10,000 square meters.
We have to find the area of a region such that a probability of at least two cacti in the region is 0.9

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