Question

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​ self-driving 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   0.352
1   0.445
2   0.179
3   0.024

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, not every probability is between 0 and 1 inclusive.

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.

A.

μ = ? ​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. σ = ? adult(s) ​(Round to one decimal place as​ needed.)

B. The table does not show a probability distribution.

Answer 1

Solution :

x	P(x)	x * P(x)	x2 * P(x)
0	0.352	0	0
1	0.445	0.445	0.445
2	0.179	0.358	0.716
3	0.024	0.072	0.216
Sum	1	0.875	1.377

A. Yes, the table shows a probability distribution.

Mean = = X * P(X) = 0.875 = 0.9

Standard deviation =

=X ² * P(X) - ²

=  1.37 - 0.875²

= 1.4