A poll showed that when a sample of people in a certain country were asked whether they were thriving, struggling, or suffering, about 47% said they were thriving. Complete parts (a) through (h) below. a. Assuming the sample size was 800, how many in the sample said they were thriving? Assuming the sample size was 800, 376 in the sample said they were thriving. (Round to the nearest integer as needed.) b. Is the sample size large enough to apply the Central Limit Theorem? Explain. Assume the other conditions are met. Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to the nearest integer as needed.) A. Yes, the sample size is large enough, since the expected number of successes is 377 and the expected number of failures is 424. both of which are greater than or equal to 10. OB. Yes, the sample size is large enough, since the estimated standard error is, which is greater than or equal to 10. OC. No, the sample size is not large enough, since the expected number of successes is and the expected number of failures is at least one of which is less than 10. OD. No, the sample size is not large enough, since the estimated standard eror is ,which is less than 10. c. Find a 95% confidence interval for the proportion that said they were thriving. The 95% confidence interval is (OO- (Round to three decimal places as needed.) d. Find the width of the interval you found in part (c) by subtracting the lower limit from the upper limit. The width of the interval is O. (Round to three decimal places as needed.) e. Now assume the sample size was 3200. How many would have said they were thriving? Assuming the sample size was 3200, O would have said they were thriving. (Round to the nearest integer 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.
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