Question

Groups of adults are randomly selected and arranged in groups of three. The random variable x is the number in the group who say that they would feel comfortable in a​ self-driving vehicle. 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	0.351
	1	0.427
	2	0.200
	3	0.022

Does the table show a probability​ distribution? Select all that apply.

A.​Yes, the table shows a probability distribution.

B.No, the sum of all the probabilities is not equal to 1.

C.No, not every probability is between 0 and 1 inclusive.

D.​No, the random variable x is categorical instead of numerical.

E.No, the random variable​ x's number values are not associated with probabilities.

Find the mean of the random variable x. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.μ =........nothing adult(s) ​(Round to one decimal place as​ needed.)

B.The table does not show a probability distribution.

Find the standard deviation of the random variable x. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.sigma σ= .....nothin gadult(s) ​(Round to one decimal place as​ needed.)

B.the table does not show a probability distribution.

Answer 1

X	P(X)	X*P(X)	X² * P(X)
0	0.35100	0.000	0.000
1	0.42700	0.427	0.427
2	0.20000	0.400	0.8000
3	0.0220	0.0660	0.1980

	P(X)	X*P(X)	X² * P(X)
total sum =	1	0.893	1.43

A.​Yes, the table shows a probability distribution.

µ=mean = E[X] = Σx*P(X) =            0.9

=============

E [ X² ] = ΣX² * P(X) =            1.4250
          
variance = E[ X² ] - (E[ X ])² =            0.6276
          
std dev = √(variance) =            0.792 ≈ 0.8