A study of green sea turtles discovered that the curved carapace (shell) length
ID: 3050740 • Letter: A
Question
A study of green sea turtles discovered that the curved carapace (shell) length of these turtles is approximately normally distributed with mean 57.2 centimeters and standard deviation 11.9 centimeters.
a. The minimum and maximum size limits for captured turtles in the legal marine turtle fishery are 41cm and 63cm, 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?
Explanation / Answer
Mean = 57.2cm
Standard deviation = 11.9 cm
P(X < A) = P(Z < (A - mean)/ standard deviation)
A) P(capturing a turle that is considered illegal) = P(X < 41) + P(X > 63)
= P(X < 41) + 1 - P(X < 63)
= P(Z < (41 - 57.2)/11.9) + 1 - P(Z < (63 - 57.2)/11.9)
= P(Z < -1.36) + 1 - P(Z < 0.49)
= 0.0869 + 1 - 0.6879
= 0.6010
B) P(X > L) = 0.02
P(X < L) = 1 - 0.02 = 0.98
P(Z < (L-57.2)/11.9) = 0.98
(L - 57.2)/11.9) = 2.05
L = 81.595cm
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