Chapter 08, Section 8.2, Intelligent Tutoring Problem 017 Determine the sample size needed to obtain an estimate of u if the margin of error E = 0.05, o = 0.90, and the confidence level is 99% (use zo.005 = 2.57). Use Table IV in Appendix C to compute the probabilities. Recall the following definitions from section 8.3 of the text. Given the confidence level and the standard deviation of the population, the sample size that will produce a predetermined margin of error E of the confidence interval estimate of u is n = E2 where the value of z is obtained from the standard normal distribution (Table IV in Appendix C or by calculator) and the quantity zo; is called the Margin of Error and is denoted by E. Furthermore, o = is the Vn standard deviation of x. Alternatively, To obtain z from a graphing calculator, we use the formula z = invNorm(1 - a/2, p, o) where p is the mean and o is the standard deviation of the normal distribution. For the standard normal distribution p = 0 and o = 1. Recall that in general z = invNorm("area to left of z", p, o). Chapter 08, Section 8.2, Intelligent Tutoring Problem 017 It is given that E = 0.05 and o = 0.90. (a) Find a for 99% confidence level. (b) Find 1 - a/2. 1 - a/2 = (c) Find for a 99% confidence level. Za/2 Za/2

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Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.