Let the random variable x represent the number of automobiles thata top salesper

Question

Let the random variable x represent the number of automobiles thata top salesperson will sell to a corporate client. The onlypossible values for x are 0, 1, 2 and the proabilities for each canbe calculated from the formula:

P(X) = .5 - (x/6) where X=0,1, or 2

a) Construct the probability distribution of the variable x.Express to 4 decimal places of accuracy.
b) Calculate the mean of this probability distribution.
c) Calculate the standard devaiation of the probabilitydistribution.
d) What is the probability that a randomly selected salespersonwill sell i. at least one automobile to a corporate client, ii. atmost 1 automobile to a corporate client, exactly 1 automobile to acorporate client?

a) for 0 i have .5 for 1 i have .3333 for 2 i have .1667
b) for the mean i have .6667
c) for this i have .5556
d) STUCK HERE not sure where i am grabbing this calculationfrom

Explanation / Answer

A) (You got this right) X 0 1 2 P(X) .5000 .3333 .1667 B) (You got this right) Mean=E(X)=0(.5000)+1(.3333)+2(.1667)=.6667 C) (You got this wrong) Standard Deviation = variance Variance = .5(0-.6667)^2 + .3333(1-.6667)^2 + .1667(2-.6667)^2 =.5556

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