Download Review #2 - PCHS AP Statistics

Chapter 6 Review
1. If the individual outcomes of a phenomenon are uncertain, but there is nonetheless a regular
distribution of outcomes in a large number of repetitions, we say the phenomenon is
A) random.
B) predictable.
C) deterministic.
D) probable.
E) none of the above.
2. The probability of any outcome of a random phenomenon is
A) the precise degree of randomness present in the phenomenon.
B) the proportion of a very long series of repetitions in which the outcome occurs.
C) either 0 or 1, depending on whether or not the phenomenon can actually occur.
D) any number, as long as it is a value between 0 and 1.
E) impossible to determine if the phenomena is truly random.
3. When two coins are tossed, the probability of getting two heads is 0.25. This means that
A) of every 100 tosses, exactly 25 will have two heads.
B) the odds against two heads are 4 to 1.
C) in the long run, the average number of heads is 0.25.
D) in the long run two heads will occur on 25% of all tosses.
4. If the knowledge that an event A has occurred implies that a second event B cannot occur, the
events A and B are said to be
A) independent.
B) disjoint.
C) mutually exhaustive.
D) the sample space.
E) complementary.
5. An assignment of probability must obey which of the following?
A) The probability of any event must be a number between 0 and 1, inclusive.
B) The sum of all the probabilities of all outcomes in the sample space must be exactly 1.
C) The probability of an event is the sum of the outcomes in the sample space which make up
the event.
D) All of the above.
E) A and B only.
Use the following to answer questions 6-7:
Event A occurs with probability 0.2. Event B occurs with probability 0.8.
6. If A and B are disjoint (mutually exclusive), then
A) P(A and B) = 0.16.
B) P(A or B) = 1.0.
C) P(A and B) = 1.0.
D) P(A or B) = 0.16.
E) Both A and B are true.
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7. If A and B are independent, then
A) P(A and B) = 0.16.
B) P(A or B) = 1.0.
C) P(A and B) = 1.0.
D) P(A or B) = 0.16.
E) both A and B are true.
Use the following to answer questions 8-9:
In a particular game, a fair die is tossed. If the number of spots showing is either four or five, you win $1.
If the number of spots showing is six, you win $4. And if the number of spots showing is one, two, or
three, you win nothing. You are going to play the game twice.
8. The probability that you win $4 both times is
A) 1/6.
B) 1/3.
C) 1/36.
D) 1/4.
E) 1/12.
9. The probability that you win at least $1 both times is
A) 1/2.
B) 4/36.
C) 1/36.
D) 1/4.
E) 3/4.
Use the following to answer questions 10-11:
Ignoring twins and other multiple births, assume that babies born at a hospital are independent events
with the probability that a baby is a boy and the probability that a baby is a girl both equal to 0.5.
10. The probability that the next five babies are girls is
A) 1.0.
B) 0.5.
C) 0.1.
D) 0.0625.
E) 0.03125.
11. The probability that at least one of the next three babies is a boy is
A) 0.125.
B) 0.333.
C) 0.667.
D) 0.750.
E) 0.875.
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12. In a certain town, 50% of the households own a cellular phone, 40% own a pager, and 20% own
both a cellular phone and a pager. The proportion of households that own neither a cellular phone
nor a pager is
A) 0%.
B) 10%.
C) 30%.
D) 70%.
E) 90%.
13. Suppose that A and B are two independent events with P(A) = 0.2 and P(B) = 0.4.
P(A  B) is
A) 0.08.
B) 0.12.
C) 0.44.
D) 0.52.
E) 0.60.
14. Suppose that A and B are two independent events with P(A) = .2 and P(B) = .4. P(A  B) is
A) 0.08.
B) 0.12.
C) 0.40.
D) 0.52.
E) 0.60.
15. The probability that a randomly chosen woman aged 20 to 24 is married is .35; the probability
that she is widowed or divorced is .03. What is the probability that such a woman has never been
married?
A) .72
B) .38
C) .62
D) .65
Use the following to answer question 16:
An event A will occur with probability 0.5. An event B will occur with probability 0.6. The probability
that both A and B will occur is 0.1.
16. The conditional probability of A given B
A) is 0.5.
B) is 0.3.
C) is 0.2.
D) is 1/6.
E) cannot be determined from the information given.
17. Event A occurs with probability 0.8. The conditional probability that event B occurs, given that A
occurs, is 0.5. The probability that both A and B occur
A) is 0.3.
B) is 0.4.
C) is 0.625.
D) is 0.8.
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1. Here is the assignment of probabilities that describes the age (in years) and the sex of a
randomly selected American student.
Age
Male
Female
14-17
.01
.01
18-24
.30
.30
25-34
.12
.13
≥35
.04
.09
a. What is the probability that the student is a female?
b. What is the conditional probability that the student is a female given that the student is at
least 35 years old?
c. What is the probability that the student is either a female or at least 35 years old?
2. A blood disease is found in 2% of the persons in a certain population. A new blood test will
correctly identify 96% of the persons with the disease and 94% of the persons without disease.
a. What is the probability that a person does not have the disease?
b. What is the probability that a person is correctly identified?
c. What is the probability that a person who is identified as having the disease actually has the
disease?
3. A company is considering implementing one of two quality control plans for monitoring the weights of
automobile batteries that it manufactures. If the manufacturing process is working properly, the battery
weights are approximately normally distributed with a specified mean and standard deviation.
Quality control plan A calls for rejecting a battery as defective if its weight falls more than 2 standard
deviations below the specified mean.
Quality control plan B calls for rejecting a battery as defective if its weight falls more tha 1.5
interquartile ranges below the lower quartile of the specified population.
Assume the manufacturing process is under control.
a. What proportion of batteries will be rejected by plan A?
b. What is the probability that at least 1 of 2 randomly selected batteries will be rejected by plan A?
c. What proportion of batteries will be rejected by plan B?
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