Question

Problem 4. Wildlife biologists believe that the weights of adult trout can be described by a Normal model. They collect data from fishermen, finding that 22% of the trout caught were thrown back because they were below the 2-pound minimum, and only 6% weighed over 5 pounds. Calculate mean and standard deviation of the weight of adult trout? (5 Points)

Answer 1

solution - oriven that Let x = weight of adults that Homean o - Standard deviation consider, we have PC x22 2 = 0:22 | |- P (x – 2) = 22 PCX > 2 ) = 1 - 2 PATH> 2 ) =1-0-22 P (2>-(2-4)) 20122 such that see standard nomal table porobablity is 0.22 - (244) = 0:44

Therefore H-01770 = 2 = 0 similarly, from second statement, P (x > 5 ) = 0.0 6 . Plas 5-) =0.06 the see standard normal table such that probabieity is 0.06, we get 5-H=1-55 4+1550=5 > ☺ By solving equation and equation ③ we get M = 2.9956 and o=12931

Hence, mean of the weight of adult torout The standard deviation of of the weight adut trout is" 1.291 - X Thank you