**Instructions:**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. \( \mu = \) [ ] adult(s) (Round to one decimal place as needed.) - ○ B. The table does not show a probability distribution.2. 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. \( \sigma = \) [ ] adult(s) (Round to one decimal place as needed.) - ○ B. The table does not show a probability distribution. **Probability Distribution Example: Self-Driving Vehicle Comfort**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.**Table: Probability of Comfort in Self-Driving Vehicles**| \( x \) | \( P(x) \) ||---|---|| 0 | 0.359 || 1 | 0.448 || 2 | 0.170 || 3 | 0.023 |**Question:**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 sum of all the probabilities is not equal to 1.- **D.** No, not every probability is between 0 and 1 inclusive.- **E.** No, the random variable \( x \) is categorical instead of numerical.**Analysis**:- Verify if the given probabilities add up to 1: \( 0.359 + 0.448 + 0.170 + 0.023 = 1.000 \).- Verify that each probability is between 0 and 1.The requirements for a probability distribution are satisfied; therefore, option A is correct.

Formula Used: Mean μ = E(X) = ∑X·P(X) Standard deviation σ = EX2-EX2 Where, EX2 = X2·P(X)

Answered: Groups of adults are randomly selected…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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