Question

Consider the following mathematical model used to predict the mass of a single largemouth fish (bass) caught from a fish population present in a lake:

Fish Mass (lb_m) = 11 – [Random(1,100)]^½

Where the function Random (1,100) returns any integer between 1 and 100 with equal probability for a particular fish caught. Based on this model, what can you say about:

a. The range of fish mass predicted by the model?

b. Does the model predict a Normal (aka Gaussian, bell curve) distribution of fish mass? Why or why not?

c. Does the model seem reasonable for prediction of the mass of a fish? Why or why not?

Answer 1

sample(100,1,TRUE) is a code in R for random integer generation

> sample (100,1, TRUE) [1] 83 > sample(100,1,TRUE) [1] 50 > sample(100,1,TRUE) [1] 69 > sample(100,1,TRUE) >FM-11-sqrt (sample (100,1, TRUE) FM [1] 2.455996 > #now run the same for 100 values of FM a large enough sample to draw a curve > #now run the same for 100 values of FM a large enough sample to draw a curve > for(i in 1:100) +FM[i]-11-sqrt (sample(100,1,TRUE) FM [1] 4.835586 5.255437 4. 519259 2.814647 3.189750 1.834849 5. 614835 7.394449 9.000000 1.202041 6.757359 [12] 2.397675 3. 651531 2.055728 3.062746 4.000000 1.202041 3.189750 8.171573 8. 354249 2. 937742 5. 522774 [23] 5.900980 4. 366750 7.000000 1.780456 2. 693376 3.000000 2.514719 1. 356349 2.753789 4. 835586 5.900980 34] 5.000000 1. 356349 7.535898 1.356349 4.442561 1.672621 2.000000 1.780456 4.917237 7.127017 3.788897 [45] 5.900980 9. 585786 9.267949 6.757359 4.519259 2. 937742 2.455996 1.100505 2.455996 4. 366750 8. 354249 [56] 9.585786 1.050126 2. 339746 2.339746 6.101021 6.101021 7.127017 6. 757359 3.583802 4.000000 5.708497 [67] 4.291796 4.755002 3.062746 5.708497 2. 633400 4. 291796 2.814647 2.111806 2.225036 6.101021 4.755002 78] 3.000000 6.000000 3. 384227 2.225036 2.753789 4.835586 2.168239 6.417424 3. 318854 7.535898 5.900980 189] 4.217670 5.169048 3.651531 5.900980 4.755002 2.455996 2.055728 8.000000 4. 675445 4. 596876 4.755002 [100] 1. 304640 > mean (FM) [1] 4.342698 > sd(FM) [1] 2.171981 > boxplot (FM) > range(FM) [1] 1.050126 9. 585786 > summary (FM) Min. 1st Qu. Median Mean 3rd Qu Max. 1.050 2. 500 4.292 4.3435.901 9.586 > plot(FM) #Plotting to see the trend > #As we can see that there is no trend in the data and so we can't predict the mass of a fish here represent ed by FM. As the random number generation makes it difficult to predict.so we can say that the model doen't seem reasonable for prediction of the mass of a fish (FM) > #The model has mean 4.34 and sd = 2.17 and so most of the observation falls between mean +/- 3*sd and so we can say that the distribution > mean(FM)-3 sd(FM) 1]2.173247 > mean(FM)+3#5d(FM) [1] 10. 85864 is normal

8 6 4 2

a)Range = 1.050126 to 9.585786 {may differ for you based upon the random numbere generatede by you}

Oo oo0o CN 0 20 40 60 80 100 Index

b)The model has mean 4.34 and sd = 2.17 and so most of the observation falls between mean +/- 3*sd and so we can say that the distribution is normal
mean-3*sd=2.173247
mean+3*sd=10.85864

c)As we can see that there is no trend in the data and so we can't predict the mass of a fish here represented by FM. As the random number generation makes it difficult to predict.So we can say that the model doen't seem reasonable for prediction of the mass of a fish (FM).

Hope the above answer has helped you in understanding the proble. Please upvote the ans if it has really helped you. Good Luck!!