Aquatic Biology (Vol. 9, 2010) studied green sea turtles inhabiting the Grand Cayman South Sound lagoon. Researchers discovered that the curved carapace (shell) length of these turtles is approximately normally distributed with mean 55.7 centimeters and standard deviation 11.5 centimeters. Complete parts a and b below. a. The minimum and maximum size limits for captured turtles in the legal marine turtle fishery are 44 cm and 60 cm, respectively. How likely are you to capture a green sea turtle that is considered illegal? The probability is .5087 . (Round to four decimal places as needed.) b. What maximum limit, L, should be set so that only 10% of the turtles captured have shell lengths greater than L? L= cm (Round to two decimal places as needed.)
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
find part b
![**Aquatic Biology (Vol. 9, 2010) Study on Green Sea Turtles in the Grand Cayman South Sound Lagoon**
Researchers studied the curved carapace (shell) length of green sea turtles and found it to be approximately normally distributed, with a mean of 55.7 centimeters and a standard deviation of 11.5 centimeters.
**Tasks:**
**a. Probability of Capturing a Turtle Outside Legal Size Limits**
The legal size limits for capturing turtles in the marine turtle fishery are set at a minimum of 44 cm and a maximum of 60 cm. Calculate the probability of capturing a green sea turtle whose size is considered illegal (either less than 44 cm or more than 60 cm).
- **The probability is:** 0.5087 (Round to four decimal places as needed.)
**b. Determining the Maximum Shell Length Limit (L)**
Find the maximum limit, L, that should be set so that only 10% of the turtles captured have shell lengths greater than L.
- **L =** [Blank] cm (Round to two decimal places as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8e803b3c-73d2-4762-ae70-129489ba72a5%2Fe2e48c9d-d20e-45cc-af2e-83a9991dbe2b%2Fcoeyas9_processed.png&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
