12/14/09



12/14/09

AP Statistics

Review for test 2

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Name:________________________________

1. A plumbing contractor obtains 60% of her boiler circulators from a company whose defect rate is 0.005, and the rest from a company whose defect rate is 0.010. What is the probability that the circulators can expected to be defective? If a circulator is defective what is the probability that it came from the first company?

(A) .0070, .429 (B) .0070, .600 (C) .0074, .600 (D) .0075, .600 (E) .0150, .571

2. Given the` probabilities P(A) = .3 and P(B) = .2, what is the probability of P(A U B) if A and B are mutually exclusive? If A and B are independent? If B is a subset of A?

(A) .44, .5, .2 (B) .44, .5, .3 (C) .5, .44, .2 (D) .5, .44, .3 (E) 0, .5, .3

3. In the following table, what value for n results in a table showing perfect independence?

|40 |60 |

|50 |n |

(A) 30 (B) 50 (C) 70 (D) 75 (E) 100

4. Suppose that for a certain Caribbean island in any 3 year period the probability of a major hurricane is .25, the probability of water damage is .44, and the probability of both a hurricane and water damage is .22. What is the probability of water damage given that there is a hurricane?

(A) .47 (B) .5 (C) .69 (D) .88 (E) .91

5. Which of the following are true statements?

I. The probability of an event is always at least 0 and at most 1.

II. The probability that an event will happen is always 2 minus the probability that it won’t happen.

III. If two events cannot occur simultaneously, the probability that at least one will occur is the sum of the respective probability of the two events.

(A) I and II (B) I and III (C) II and III (D) I, II, and III (E) none of the above

6. In the November 27, 1994, issue of Parade magazine, the “ask Marilyn” section contained this question: “Suppose a person was having two surgeries performed at the same time. If the chance of success for surgery A are 85%, and the chances of success for surgery B are 90%, what are the chances that both would fail?” What do you think Marilyn’s solution; (.15)(.10) = .015 0r 1.5?

A) Her solution is mathematically correct but not explained very well.

B) Her solution is both mathematically correct and intuitively obvious.

C) Her use of complementary events is incorrect.

D) Her use the general addition formula is incorrect.

E) She assumed independence of events, which is most likely wrong.

7. An experiment has three mutually exclusive outcomes, A, B and C. If P(A) = 0.12, P(B) = .61, and P(C) = 0.27, which of the following must be true?

I. A and C are independent.

II. P(A ∩ B) = 0

III. P(B U C) = P(B) + P(C)

8. The table below shows the results of a survey of the drinking and smoking habits of 1200 college students.

Drink Beer Don’t Drink

|Smoke |315 |165 |

|Don’t Smoke |585 |135 |

What is the probability that a smoker drinks?

A) 315 (B) 315 (C) 480 (D) 900 (E) 0

480 1200 1200 1200

9. Based on the table in (8), what is the probability that a student drink if he or she is a smoker?

(A) 315 (B) 315 (C) 480 (D) 900 (E) 0

480 1200 1200 1200

10. A coin is flipped three times, what is the probability of getting at least two tails?

(A) ½ (B) ¾ (C) 3/8 (D) 5/8 (E) 1

Free-Response

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1. An AP Statistics student takes a random survey of 100 high school teachers and classified department affiliation versus music preference. The result are as follows;

Classical Country Jazz

|Humanties | 15 |5 |20 |

|Mathematics |10 |15 |10 |

|Fine Arts |15 |5 |5 |

A. What the probability that a teacher selected at random from this ample is a Fine Arts teacher who prefers country music?

B. What is the probability that a teacher selected at random from this sample is a math teacher if that teacher prefer Jazz?

C. What is the probability that a teacher selected at random from this sample is a humanities teacher or a teacher that prefers Classical?

D. Are the events that a teacher prefers Jazz and the event that a teacher is from the Math department independent?

2. A printing company takes new jobs on a first come first serve basis. Typically, 25% of the orders are small, taking 3 hours to finish, 305 of the orders take 8 hours to finish, 35% take 12 hours, and 10% take 20 hours.

a. Suppose in any given week that when the total number of hours reaches or exceeds 40, no further orders will be taken. Explain how you would use simulation with a random number table to estimate the distribution of the number of new jobs the firm takes on each week and the distribution of the number of job hours the firm accepts each week.

b. Run three trials of your simulation using the random number table below. Give your results, explaining you procedure.

84177 06757 17613 51506 81435 41050 92031 06449 05059 59884 31180 53115 84469 94868 57967 05811 84514 75011 13006 63395 55041 15866 06589 13119 71020 85940 91932 06488 74987 32100

3. Explain the difference between

a. Mutually exclusive events and Independent events

b. The law of large number and the law of averages

c. Theoretical probability and Empirical Probability

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