Homework: Week 4- Chapter 5 &6 Score: 0 of 1 pt x5.3.42-T Save 10 of 15 (12 comp

Question

Homework: Week 4- Chapter 5 &6 Score: 0 of 1 pt x5.3.42-T Save 10 of 15 (12 complete) HW Score: 63.06%, 9.46 of 15 pts Question Help A study of green sea turtles discovered that the curved carapace (shell) length of these turtles is approximately normally distributed with mean 51.6 centimeters and standard deviation 12.5 centimeters. a. The minimum and maximum size limits for captured turtles in the legal marine turtle fishery are 37 cm and 57 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 5% of the turtles captured have shell lengths greater than L? a. The probability of catching a green turtle that is considered illegal is Round to three decimal places as needed.)

Explanation / Answer

P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = 51.6 cm

Standard deviation = 12.5 cm

P(illegal) = P(X < 37) + P(X > 57)

= P(X < 37) + 1 - P(X < 57)

= P(Z < (37 - 51.6)/12.5) + 1 - P(Z < (57 - 51.6)/12.5)

= P(Z < -1.17) + 1 - P(Z < 0.43)

= 0.1210 + 1 - 0.6664

= 0.4546

b) P(X > L) = 0.05

P(X < L) = 1 - 0.05 = 0.95

P(Z < (L - 51.6)/12.5) = 0.95

(L - 51.6)/12.5 = 1.645

L = 72.1625

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