Asociologist randomly selects single adults for different groups of three, and the random variable x is the number in the group who say that the most fun way to flirt is in person. determine whether a probability distribution is given. if a probability distribution is given, find its mean and standard deviation. if a probability distribution is not given, identify the requirements that are not satisfied. x p(x) 0 0.087 1 0.328 2 0.416 3 0.169 does the table show a probability distribution? select all that apply. a. yes, the table shows a probability distribution. b. no, the random variable x's number values are not associated with probabilities. c. no, the random variable x is categorical instead of numerical. d. no, the sum of all the probabilities is not equal to 1. e. no, not every probability is between 0 and 1 inclusive.

A. Yes, the table shows a probability distribution.

Step-by-step explanation:

In a probability distribution, none of the values can be negative or over 1.  Additionally, all of the values must sum to 1.

Our probabilities are:

0.087; 0.328; 0.416; and 0.169.  None of these are negative and none are over 1.

0.087+0.328+0.416+0.169 = 1.00; this means that this is a probability distribution.

B. y = 2x - 2

E.

F.

Step-by-step explanation:

The equation of the line can be found using either the point-slope equation or the slope-intercept equation.

✔️Equation of the line in point-slope using the slope and the coordinates of the point (4, 6):

Slope = m = change in y/change in x

Using (4, 6) and (-1, -4),

m = (-4 - 6)/(-1 - 4)

m = -10/-5

m = 2

Substitute m = 2, and (a, b) = (4, 6) into the point-slope equation form

Thus:

✔️Equation of the line in point-slope using the slope and the coordinates of the point (-1, -4):

Slope = m = 2

Substitute m = 2, and (a, b) = (-1, -4) into the point-slope equation form

Thus:

✔️Equation of the line in slope-intercept form, y = mx + b

Where,

m = slope = 2

b = y-intercept = -2 (the point where the line intercepts the y-axis)

Thus, substitute m = 2 and b = -2 into y = mx + b

y = 2x + (-2)

y = 2x - 2