**Exercises** **6.1 Vegetarian college students.** Suppose that 9% of college students are vegetarians. Determine if the following statements are true or false, and explain your reasoning. (a) The distribution of the sample proportions of vegetarians in random samples of size 60 is approximately normal since \( n \geq 30 \). (b) The distribution of the sample proportions of vegetarians in random samples of size 50 is right skewed. (c) A random sample of 125 college students where 12% are vegetarians would be considered unusual. (d) A random sample of 250 college students where 12% are vegetarians would be considered unusual. (e) The standard error would be reduced by one-half if increased the sample size from 125 to 250. **6.2 Young Americans, Part I** About 77% of young Americans think they can achieve the American dream. Determine if the following statements are true or false, and explain your reasoning. (a) The distribution of sample proportions of young Americans who think they can achieve the American dream in samples of size 60 is left skewed. (b) A random sample of 1219 young Americans where 75% think they can achieve the American dream would be considered unusual. (c) A random sample of 60 young Americans where 70% think they can achieve the American dream would be considered unusual. (d) The distribution of the sample proportions of young Americans who think they can achieve the American dream is approximately normal since \( n \geq 30 \). --- There are no graphs or diagrams in the text.

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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.