Let the random variable x represent the number of automobile

Let the random variable x represent the number of automobiles that a top salesperson will sell to a corporate client. The only possible values for x are 0, 1 and 2, and the probabilities for each of these values may be calculated from the formula P(x) = 0.5 - (x/6) where x = 0, 1 or 2

a. Construct the probability distribution of the variable x. Express your probabilities to 4 decimal places of accuracy.

b. Calculate the mean of this probability distribution.

c. Calculate the standard deviation of this probability distribution.

d. What is the probability that a randomly selected top salesperson will sell

i. at least 1 automobile to a corporate client?

ii. at most 1 automobile to a corporate client?

iii. exactly 1 automobile to a corporate client?

Solution

A) (Y)

B)
Mean=E(X)=0(.5000)+1(.3333)+2(.1667)=.6667

C)
Standard Deviation = ?variance
Variance = .5(0-.6667)^2 + .3333(1-.6667)^2 + .1667(2-.6667)^2 =.5556 <-- You calculated this
Standard deviation = ?variance = ?.5556 = .7454