Question

Let X represent the number of homes a real estate agent sells during a given month. Based on previous sales? records, she estimates that

Upper P left parenthesis 0 right parenthesis equals 0.63P(0)=0.63?,

Upper P left parenthesis 1 right parenthesis equals 0.24P(1)=0.24?,

Upper P left parenthesis 2 right parenthesis equals 0.09P(2)=0.09?,

Upper P left parenthesis 3 right parenthesis equals 0.03P(3)=0.03?,

Upper P left parenthesis 4 right parenthesis equals 0.01P(4)=0.01?,

with negligible probability for higher values of x.a. Explain why it does not make sense to compute the mean of this probability distribution as

left parenthesis 0 plus 1 plus 2 plus 3 plus 4 right parenthesis divided by 5 equals 2.0(0+1+2+3+4)/5=2.0.

b. Find the correct mean and interpret.

a. Choose the reason why the mean is not the simple average of the possible values.

A.

The mean should be computed by averaging the? probabilities, not the possible values.

B.

The probabilities of each possible value are not all the same.

Your answer is correct.

C.

There are not enough possible values of x to compute the mean.

D.

The possible value of 0 skews the mean when computed in this fashion.

b. Select the correct choice below and fill in the answer box to complete your choice.

?(Type an integer or a decimal. Do not? round.)

A.

The? long-term average number of homes the real estate agent expects to sell each month is

nothing.

B.

The real estate agent will sell

nothing

?home(s) this month.

Answer 1

a) The correct mean is not computed by simply taking the arithmetic average of the different values of X but by taking the weighted average weighted by the frequency for each X. Therefore the correct mean here is computed as:

Therefore 0.55 is the required mean value here.

Also the reason , correct answer is B

The probabilities of each possible value are not all the same, therefore simple averages cannot be used.

b) Now the interpretation of the mean here of 0.55 is that the long term average number of homes the real estate expected to see is 0.55 Therefore A is the correct answer here.