Which of the following is always true? choose the correct answer below. a. in a symmetric and bell-shaped distribution, the mean, median, and mode are the same. b. the mean and median should be used to identify the shape of the distribution. c. data skewed to the right have a longer left tail than right tail. d. for skewed data, the mode is farther out in the longer tail than the median.

A. In a symmetric and bell-shaped distribution, the mean, median, and mode are the same.

Symmetric distribution is a situation in which the mean, median, and mode are located at the same point and the values of the variables are at regular frequencies. Unlike the skewed distribution, the symmetric distribution does not skew.

The symmetric distribution is usually shaped like a bell curve when depicted on a graph. If a line is drawn down the middle of the graph, the two sides will mirror each other.

The bell curve indicates that the data are symmetric and thus we can make possible expectations according to the probability that the result will be located to the left or right of the center within a range, once we have the deviation inherent in it. Data to measure quantity.

A bell curve graph always depends on two factors:  

(1) Mean: It says about the position of center always.

(2) Standard deviation: It gives the value of the width and height of the bell.

Therefore, we can conclude from the given options, only option (A) is correct.

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.