An elevator has a placard stating that the maximum capacity is 1680 lb-10 passengers. So, 10 adult male passengers can have a mean weight of up to 1680/10= 168 pounds. If the elevator is loaded with 10 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 168 lb. (Assume that weights of males are normally distributed with a mean of 178 lb and a standard deviation of 28 lb.) Does this elevator appear to be safe? The probability the elevator is overloaded is. (Round to four 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.
![**Probability and Elevator Safety**
**Elevator Loading Analysis**
An elevator has a placard stating that the maximum capacity is 1680 lb for 10 passengers. This means that 10 adult male passengers can have a mean weight of up to 1680 / 10 = 168 pounds each. We need to find the probability that the elevator is overloaded if it is loaded with 10 adult male passengers.
*Problem Statement*:
If the elevator is loaded with 10 adult male passengers, what is the probability that it is overloaded due to the passengers having a mean weight greater than 168 lb? (Assume weights of males are normally distributed with a mean of 178 lb and a standard deviation of 28 lb.) Does this elevator appear to be safe?
*Solution*:
The probability the elevator is overloaded is **[Box for Answer]**.
*Note*: Remember to round your answer to four decimal places as needed.
Understanding Normal Distribution:
A normal distribution is a continuous probability distribution where data around a mean is symmetrically spread. For this scenario, recognizing the mean (178 lb) and standard deviation (28 lb) is crucial in determining the likelihood of the elevator being overloaded.
To solve this, you'll typically use the concept of a normal distribution probability calculation, focusing on the sample mean and the standard error.
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