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 selfdriving 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.
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
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