A study of green sea turtles discovered that the curved carapace (shell) length

Question

A study of green sea turtles discovered that the curved carapace (shell) length of these turtles is approximately normally distributed with mean 54.3 centimeters and standard deviation 12.9 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 10% of the turtles captured have shell lengths greater than L?

Explanation / Answer

Ans:

Given that

mean=54.3

standard deviation=12.9

a)

z(38)=(38-54.3)/12.9=-1.26

z(58)=(58-54.3)/12.9=0.29

P(illegal)=P(x<38 or x>58)=P(z<-1.26 or z>0.29)

=P(z<-1.26)+P(z>0.29)

=0.1032+0.3871=0.4903

b)P(Z>z)=0.1

P(Z<=z)=1-0.1=0.9

z=1.282

L=54.3+1.282*12.9

L=70.84

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