5. The lengths of walleye in a lake are normally distributed with mean 21 inches and standard deviation 8 inches. a. What percentage of walleye have length between 3 inches 31 inches? b. DNR decides to allow anglers to keep any walleye in the top 10%. What length a walleye should be in order to keep?
5. The lengths of walleye in a lake are normally distributed with mean 21 inches and standard deviation 8 inches. a. What percentage of walleye have length between 3 inches 31 inches? b. DNR decides to allow anglers to keep any walleye in the top 10%. What length a walleye should be in order to keep?
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:### Problem 5
The lengths of walleye in a lake are normally distributed with a mean of 21 inches and a standard deviation of 8 inches.
#### Questions:
a. **What percentage of walleye have lengths between 3 inches and 31 inches?**
b. **DNR decides to allow anglers to keep any walleye in the top 10%. What length should a walleye be in order to keep it?**
#### Explanation:
The problem includes two small bell-shaped curves, which represent normal distribution graphs. The first graph is related to part (a) and illustrates the shaded area between two points, indicating the percentage of walleye lengths between 3 and 31 inches. The second graph, related to part (b), shows the extreme right portion shaded, representing the top 10% of walleye lengths.
The normal distribution is a continuous probability distribution that is symmetrical around its mean. The percentage of observations falling within a particular range can be determined using the properties of the distribution and statistical tables or software.
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