Question

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 |
0.0940.094 |
||||

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

Answer #1

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 + 2^{2} * 0.403 + 3^{2} * 0.166
- 1.6^{2}

**= 0.9**

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