A simple random sample of size n= 65 is obtained from a population with u = 57 and o = 5. (a) Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? (b) What is the sampling distribution of x? (a) Does the population need to be normally distributed for the sampling distribution of x to be approximately normally distributed? Why? (Choose the correct answer below.) O A. No because the Central Limit Theorem states that regardless of the shape of the underlying population, the sampling distribution of x becomes approximately normal as the sample size, n, increases. O B. No because the Central Limit Theorem states that only if the shape of the underlying population is normal or uniform does the sampling distribution of x become approximately normal as the sample size, n, increases. O C. Yes because the Central Limit Theorem states that only for underlying populations that are normal is the shape of the sampling distribution of x normal, regardless of the sample size, n. O D. Yes because the Central Limit Theorem states that the sampling variability of nonnormal populations will increase as the sample size increases. (b) What is the sampling distribution of x? (Choose the correct answer below.) O A. The sampling distribution of x is normal or approximately normal with H; = 57 and o; = 5. O B. The sampling distribution of x follows Student's t-distribution with u; = 57 and o: = 5. O C. The sampling distribution of x is normal or approximately normal with u; = 57 and o; =0.620. O D. The sampling distribution of x is uniform with p; = 57 and o; = 0.620. Click to select your answer.

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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.