A particular lake is known to be one of the best places to catch a certain type of fish. In this table, x = number of fish caught in a 6-hour period. The percentage data are the percentage of fishermen who caught x fish in a 6-hour period while fishing from shore. 1 3 4 or more 43% 35% 15% 6% 1% (a) Convert the percentages to probabilities and make a histogram of the probability distribution. (Select the correct graph.)
A particular lake is known to be one of the best places to catch a certain type of fish. In this table, x = number of fish caught in a 6-hour period. The percentage data are the percentage of fishermen who caught x fish in a 6-hour period while fishing from shore. 1 3 4 or more 43% 35% 15% 6% 1% (a) Convert the percentages to probabilities and make a histogram of the probability distribution. (Select the correct graph.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:A particular lake is known to be one of the best places to catch a certain type of fish. In this table, \( x \) represents the number of fish caught in a 6-hour period while fishing from shore. The percentage data reflects the proportions of fishermen who caught \( x \) fish in this time frame.
| \( x \) | 0 | 1 | 2 | 3 | 4 or more |
|-----------------|-----|-----|-----|-----|-----------|
| \% | 43% | 35% | 15% | 6% | 1% |
(a) Convert the percentages to probabilities and create a histogram of the probability distribution. (Select the correct graph.)
**Explanation:**
To convert the percentages to probabilities, divide each percentage by 100. The probabilities for catching \( x \) fish in a 6-hour period are:
- Probability of catching 0 fish: 0.43
- Probability of catching 1 fish: 0.35
- Probability of catching 2 fish: 0.15
- Probability of catching 3 fish: 0.06
- Probability of catching 4 or more fish: 0.01
**Histogram Description:**
The histogram should have the number of fish caught (\( x \)) on the x-axis and the probability on the y-axis. Each bar represents the probability of catching a specific number of fish:
- The first bar (0 fish) reaches up to 0.43.
- The second bar (1 fish) reaches up to 0.35.
- The third bar (2 fish) reaches up to 0.15.
- The fourth bar (3 fish) reaches up to 0.06.
- The last bar (4 or more fish) reaches up to 0.01.
The histogram provides a visual representation of the probability distribution of catching fish in a 6-hour period.
![(d) Compute μ, the expected value of the number of fish caught per fisherman in a 6-hour period (round 4 or more to 4). (Enter a number. Round your answer to two decimal places.)
μ = [___] fish
(e) Compute σ, the standard deviation of the number of fish caught per fisherman in a 6-hour period (round 4 or more to 4). (Enter a number. Round your answer to three decimal places.)
σ = [___] fish](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7aeb506e-af93-4768-b77e-6313e85f4e04%2Fb41ad63b-767e-4cfa-935b-9dd69dd25196%2Foyl2keq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(d) Compute μ, the expected value of the number of fish caught per fisherman in a 6-hour period (round 4 or more to 4). (Enter a number. Round your answer to two decimal places.)
μ = [___] fish
(e) Compute σ, the standard deviation of the number of fish caught per fisherman in a 6-hour period (round 4 or more to 4). (Enter a number. Round your answer to three decimal places.)
σ = [___] fish
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