A sociologist randomly selects single adults for different g

A sociologist randomly selects single adults for different groups of four and the random variable x is the number in the group who say that the most fun way to flirt is in person (based on a microsoft instant messaging survey). The ditribution of the data is given below.

A. Is this a probability distribution? Why?

B. What is the mean, and standard deviation for this distribution?

Solution

Hi! I think you mean 0.092 in P(4). Otherwise, it will not be a probability distrbution. I assumed P(4) = 0.092. Thanks!
***********************

a)

yes, because the probabilities add up to 1.

b)

Consider:

Thus,      
      
E(x) = Expected value = mean =    2.199   [ANSWER, MEAN]

Var(x) = E(x^2) - E(x)^2 =    0.995399  

Thus,

s(x) = sqrt [Var(x)] =    0.997696848   [ANSWER, STANDARD DEVIATION]