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 0.354 1 0.436 2 0.187 3 0.023

Answer 1

Answer:

It is a discrete distribution of probability, with mean = 0.879 and SD = 0.787.

Step-by-step explanation:

With the given data, it can be said we have a discrete distribution of probability.

Calculation of the mean

$\bar{X}=\sum_{i=0}^{3} P(x_{i})*x_{i} = 0.354*0+0.436*1+0.187*2+0.023*3=0.879$

Calculation of the standard deviation

$sd=\sqrt{\sum_{i=0}^{3} P(x_{i})*(x_{i}-\bar{x})^{2} } \\\\sd= \sqrt{0.354*(0-0.879)^{2} +0.436*(1-0.879)^{2}+0.187*(2-0.879)^{2}+0.023*(3-0.879)^{2}}\\\\sd=\sqrt{0.354*0.773 +0.436*0.015+0.187*1.257+0.023*4.499}\\\\sd=\sqrt{0.619}=0.787$