Question

A study of green sea turtles discovered that the curved carapace​ (shell) length of these turtles is approximately normally distributed with mean 52.6 centimeters and standard deviation 12.1 centimeters. a. The minimum and maximum size limits for captured turtles in the legal marine turtle fishery are 38 cm and 58 ​cm, respectively. How likely are you to capture a green sea turtle that is considered​ illegal? b. What maximum​ limit, L, should be set so that only 2​% of the turtles captured have shell lengths greater than​ L?

Answer 1

a)

µ =    52.6                              
σ =    12.1                              
we need to calculate probability for ,                                  
P (   38   < X <   58   )                  
=P( (38-52.6)/12.1 < (X-µ)/σ < (58-52.6)/12.1 )                                  
                                  
P (    -1.207   < Z <    0.446   )                   
= P ( Z <    0.446   ) - P ( Z <   -1.21   ) =    0.6723   -    0.1138   =    0.5585

required probability = 1-0.5585 = 0.4415 (answer)

b)

µ=   52.6  
σ =    12.1  
P(X≤x) =   0.98000  
      
z value at 0.98=   2.0537   (excel formula =NORMSINV(0.98))
z=(x-µ)/σ      
so, X=zσ+µ=   2.054   *12.1+52.6
X =   77.450   (answer)

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