Question

# A sociologist randomly selects single adults for different groups of​ three, and the random variable x...

 x ​P(x) 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. 0 0.0940.094 1 0.3370.337 2 0.4030.403 3 0.1660.166

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.

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.

muμequals=1.61.6

​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.

sigmaσequals=0.90.9

​adult(s) ​(Round to one decimal place as​ needed.)

B.

The table does not show a probability distribution.

More

Solution :

The sum of the probability is equal to 1 .

P(X) = 1

1 = 0.094 + 0.337 + 0.403 + 0.166

A.

​Yes, the table shows a probability distribution.

Mean = X * P(X)

= 0 * 0.094 + 1 * 0.337 + 2 * 0.403 + 3 * 0.166 = 1.6

Standard deviation =

=X 2 * P(X) - 2

=  0 * 0.094 + 1 * 0.337 + 22 * 0.403 + 32 * 0.166 - 1.62

= 0.9

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