Question

# Groups of adults are randomly selected and arranged in groups of three. The random variable x...

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.

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

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