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# Probability and Random Variables Multiple Choice Practice Problems for AP Statistics (page 2)

based on 3 ratings
By — McGraw-Hill Professional
Updated on Feb 3, 2011

### Solutions

1. The correct answer is (c). There are 12 values in the A and E cell and this is out of the total of 125. When we are given column E, the total is 63. Of those, 28 are C.
2. The correct answer is (b).
3. (This problem is an example of what is known as Bayes's rule. It's still conditional probability, but sort of backwards. That is, rather than being given a path and finding the probability of going along that path—P(X | B) refers to the probability of first traveling along B and then along X—we are given the outcome and asked for the probability of having gone along a certain path to get there—P(B | X) refers to the probability of having gotten to X by first having traveled along B. You don't need to know Bayes's rule by name for the AP exam, but you may have to solve a problem like this one.)

4. The correct answer is (e). If you knew that the variables "Score on Statistics Exam" and "Score on Spanish Language Exam" were independent, then the standard deviation would be given by
5. However, you cannot assume that they are independent in this situation. In fact, they aren't because we have two scores on the same people. Hence, there is not enough information.

6. The correct answer is (a).
7. The calculator answer is normalcdf(-100,3,3.4,0.3) = 0.0912. Note that answer (d) makes no sense since probability values must be non-negative (and, of course, less than or equal to 1).

8. The correct answer is (d). Because ethnic group categories are assumed to be mutually exclusive, P(Asian or Latino) = P(Asian) + P(Latino) = 32% + 11% = 43%.
9. The correct answer is (e). The situation is as pictured below:
10. From Table A, zx = 1.645 (also, invNorm(0.95) = 1.645).

Hence, . Norma would need a minimum GPA of 3.89 in order to qualify for the honor society.

11. The correct answer is (c). P(Y = 4) = . Since they are independent,
12. The correct answer is (c). The expected value is (–1)(0.6) + (1)(0.25) + (2)(0.15) = –0.05.
13. The correct answer is (d). P(at least one of the first two rolls is "Y") = P(the first roll is "Y") + P(the second roll is "Y") – P(both rolls are "Y") = . Alternatively, P(at least one of the first two rolls is "Y") = 1 – P(neither roll is "Y") = .
14. The correct answer is (b). The possible outcomes where one die shows a 4 are highlighted in the table of all possible sums:
15. There are 11 cells for which one die is a 4 (be careful not to count the 8 twice), 2 of which are 6's.

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