The average number of field mice per acre in a 6-acre wheat field is estimated to be 11. (a) Find the probability that fewer than 8 field mice are found on a given acre. (b) Find the probability that fewer than 8 field mice are found on 2 of the next 4 acres inspected. Click here to view the table of Poisson probability sums. (a) The probability that fewer than 8 field mice are found on a given acre is (Round to four decimal places as needed.) (b) The probability that fewer than 8 field mice are found on 2 of the next 4 acres inspected is (Round to four decimal places as needed.)
The average number of field mice per acre in a 6-acre wheat field is estimated to be 11. (a) Find the probability that fewer than 8 field mice are found on a given acre. (b) Find the probability that fewer than 8 field mice are found on 2 of the next 4 acres inspected. Click here to view the table of Poisson probability sums. (a) The probability that fewer than 8 field mice are found on a given acre is (Round to four decimal places as needed.) (b) The probability that fewer than 8 field mice are found on 2 of the next 4 acres inspected is (Round to four decimal places as needed.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![### Problem Description:
The average number of field mice per acre in a 6-acre wheat field is estimated to be 11.
**Tasks:**
1. **(a) Calculate the Probability for a Single Acre:**
Find the probability that fewer than 8 field mice are found on a given acre.
2. **(b) Calculate the Probability for Multiple Acres:**
Find the probability that fewer than 8 field mice are found on 2 of the next 4 acres inspected.
**Additional Resource:**
- A table of Poisson probability sums is provided to assist with these calculations.
### Question Breakdown:
1. **(a) The probability that fewer than 8 field mice are found on a given acre is:**
\[
\text{(Round to four decimal places as needed.)}
\]
2. **(b) The probability that fewer than 8 field mice are found on 2 of the next 4 acres inspected is:**
\[
\text{(Round to four decimal places as needed.)}
\]
**Instructions:**
- For both parts of the problem, utilize the Poisson probability table to sum up the probabilities of having fewer than 8 field mice.
**Understanding Poisson Distribution:**
The Poisson distribution helps in determining the probability of a given number of events happening in a fixed interval of time or space when these events occur with a known constant rate and independently of the time since the last event.
**How to Use the Poisson Table:**
- Find the corresponding probabilities for having 0, 1, 2, ..., up to 7 field mice for the given rate (11 mice/acre in this case).
- Sum these probabilities to get the final result.
**Visual Representation:**
Since this text is intended for an educational website, you could also integrate an example diagram or graph showing the Poisson distribution curve for λ (lambda) = 11, marking the cumulative probability up to 7 mice. This visual representation would help in better understanding the probability distribution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7167d01a-fc0a-4c3f-ab49-29dc29956a80%2F1abc3eba-9e16-405b-aad9-a8cc68715857%2F2dj9fus_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Description:
The average number of field mice per acre in a 6-acre wheat field is estimated to be 11.
**Tasks:**
1. **(a) Calculate the Probability for a Single Acre:**
Find the probability that fewer than 8 field mice are found on a given acre.
2. **(b) Calculate the Probability for Multiple Acres:**
Find the probability that fewer than 8 field mice are found on 2 of the next 4 acres inspected.
**Additional Resource:**
- A table of Poisson probability sums is provided to assist with these calculations.
### Question Breakdown:
1. **(a) The probability that fewer than 8 field mice are found on a given acre is:**
\[
\text{(Round to four decimal places as needed.)}
\]
2. **(b) The probability that fewer than 8 field mice are found on 2 of the next 4 acres inspected is:**
\[
\text{(Round to four decimal places as needed.)}
\]
**Instructions:**
- For both parts of the problem, utilize the Poisson probability table to sum up the probabilities of having fewer than 8 field mice.
**Understanding Poisson Distribution:**
The Poisson distribution helps in determining the probability of a given number of events happening in a fixed interval of time or space when these events occur with a known constant rate and independently of the time since the last event.
**How to Use the Poisson Table:**
- Find the corresponding probabilities for having 0, 1, 2, ..., up to 7 field mice for the given rate (11 mice/acre in this case).
- Sum these probabilities to get the final result.
**Visual Representation:**
Since this text is intended for an educational website, you could also integrate an example diagram or graph showing the Poisson distribution curve for λ (lambda) = 11, marking the cumulative probability up to 7 mice. This visual representation would help in better understanding the probability distribution.
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