Questions 6-14 are related to the following:
In the table below, x denotes the X-Tract Company's projected annual profit (in $1,000). The table also shows the probability of earning that profit. The negative value indicates a loss.
x f(x)
-200 0.03
-100 0.04
0 0.25
250 0.40
400 0.08
500 0.02
6. The probability that X-Tract will break even is,
f(x = 0) = ________.
a) 0.10
b) 0.12
c) 0.18
d) 0.25
7. What is the probability that X-Tract will be profitable? That is, f(x > 0) = _________.
a) 0.95
b) 0.75
c) 0.50
d) 0.65
8. What is the expected value of profit?
a) $234.5 thousand
b) $246.5 thousand
c) $258.0 thousand
d) $273.5 thousand
9. What is the variance of profit?
a) 20056.70
b) 20259.30
c) 29034.75
d) 21086.205
10. On average, profit (loss) amounts deviate from the expected profit by ______ thousand.
a) $143.78 thousand
b) $147.37 thousand
c) $151.06 thousand
d) $170.40 thousand
11. If we add $125 to the profit/loss column above, the new expected value of profit will be,
a) 359.5
b) 387.5
c) 393.0
d) 398.5
12. If we add $125 to the profit/loss column above, the new variance of profit will be,
a) 36297.75
b) 29034.75
c) 20797.75
d) 18632.75
13. If we quadruple the profit column above, the new expected value of profit will be.
a) 821
b) 1738
c) 938
d) 4376
14. If we quadruple the profit column above, the new variance of profit will be.
a) 82691
b) 165382
c) 248073
d) 464556