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 0.367 1 0.428 2 0.180 3 0.025 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 is categorical instead of numerical.

C. ​No, not every probability is between 0 and 1 inclusive.

D. ​No, the sum of all the probabilities is not equal to 1.

E. ​No, the random variable​ x's number values are not associated with probabilities. 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. mu equalsnothing ​adult(s) ​(Round to one decimal place as​ needed.)

Answer 1

Solution:

Given:

x	P(x)
0	0.367
1	0.428
2	0.180
3	0.025

Part a) Does the table show a probability​distribution? Select all that apply.

Yes. Since total probability is 1 and each probability is > 0.

Thus correct answer is:

A. ​Yes, the table shows a probability distribution.

Part b) Find mean and standard deviation:

Mean:

Standard Deviation:

where

thus we need to make following table:

x	P(x)	x*P(x)	x2 *P(x)
0	0.367	0	0
1	0.428	0.428	0.428
2	0.180	0.36	0.72
3	0.025	0.075	0.225

Thus

Mean:

Standard Deviation:

where

thus

_{(Round final answer to specified number of decimal places)}