A sociologist 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 0.344 2 0.415 3 0.154

Yes the table shows a probability distribution

The mean is

The  standard deviation is  

Step-by-step explanation:

From the question we are told that

The data given is

x 0 1 2 3

P(x) 0.087 0.344 0.415 0.154

Generally we can evaluate as

0 (1 * 0.344 ) (2 * 0.415) (3 * 0.154 )

=> 0 0.344 0.830 0.462

Generally we can evaluate as

0 [tex ](1^2 * 0.344 )[/tex] [tex ](2^2 * 0.415)[/tex] [tex ](3^2 * 0.154 )[/tex]

=> 0 [tex ]1.66 [/tex]

Generally the mean is mathematically represented as

Generally the standard deviation is mathematically represented as

Here is the variance which is mathematically represented as

Here

So

So