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 | 0.086 1 0.337 2 0.421 30.156 Does the table show a probability distribution? Select all that apply. A. Yes, the table shows a probability distribution. B. No, not every probability is between 0 and 1 inclusive. I C. No, the random variable x's number values are not associated with probabilities OD. No, the random variable x is categorical instead of numerical. E. No, the sum of all the probabilities is not equal to 1. 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. O A. u= adult(s) (Round to one decimal place as needed.) OB. 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. O A. Or adult(s) (Round to one decimal place as needed.) O B . The table does not show a probability distribution.

Answer 1

Solution :

x	P(x)	x * P(x)	x2 * P(x)
0	0.086	0	0
1	0.337	0.337	0.337
2	0.421	0.842	1.684
3	0.156	0.468	1.404
Sum	1	1.647	3.425

The sum of the probability is equal to 1 .

$\sum$P(X) = 1

A. Yes, the table shows a probability distribution

Mean = $\mu$ = $\sum$ X * P(X) = 1.6

Standard deviation = $\sigma$

=$\sqrt$$\sum$X ² * P(X) - $\mu$ ²

=  $\sqrt$3.425 - 1.647²

= 0.8