1. The University of North Carolina Chapel Hill received over 42,000 application for undergraduate admission for the 2019-2020 school year. Of those applicants, only 4,180 w accepted and enrolled for the school year. The high school GPA of those incoming freshmen has a Normal distribution with a mean of 4.39 and a standard deviation of o.586. [Data collected from publicly available reports at oira.unc.edu] A. Calculate the probability that a single randomly selected student has a high school GPA of 4.00 or less. B. A school counselor surveyed an SRS of 50 incoming freshman from that same school year. Calculate the mean and standard deviation of the sampling distribution of 7 for samples of size n=50. Interpret the standard deviation and be sure to check any relevant conditions.
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.
![1. The University of North Carolina Chapel Hill received over 42,000 application for
undergraduate admission for the 2019-2020 school year. Of those applicants, only 4,180 w
accepted and enrolled for the school year. The high school GPA of those incoming freshmen has a
Normal distribution with a mean of 4.39 and a standard deviation of o.586. [Data collected from
publicly available reports at oira.unc.edu]
A. Calculate the probability that a single randomly selected student has a high school GPA of
4.00 or less.
B. A school counselor surveyed an SRS of 50 incoming freshman from that same school year.
Calculate the mean and standard deviation of the sampling distribution of for samples of
size n=50. Interpret the standard deviation and be sure to check any relevant conditions.
C. What is the shape of the distribution described in part b? Justify your answer.
D. The counselor in part B obtained a sample mean of 4.0. Calculate the probability that a
random sample of 50 students produces a sample mean at or below the counselor's sample
mean.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F306d609c-8cfa-4653-b46f-ce92484d421e%2F1d460a9b-83c6-4469-a25d-effbdcbfc73c%2Fhgicfn_processed.jpeg&w=3840&q=75)
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