MC Questions for Ch. 7
Name_________________
AP STATS
Date_________Per_____
1.
The probability that a three-year-old battery still works is 0.8. A cassette recorder requires four working batteries to operate.
The state of batteries can be regarded as independent, and four three-year-old batteries are selected for the cassette recorder.
What is the probability that the cassette recorder operates, that is all four three-year-old batteries work?
A) 0.9984
B) 0.8000
C) 0.5904
D) 0.4096
E)
2.
The answer cannot be computed from the information given.
X and Y are independent random variables. Which of the following statements are TRUE?
I. Var  X  Y   Var  X   Var Y 
II. MEAN  3 X  2   3Mean  X 
III.
3.
StdDev  X  Y   StdDev  X   StdDev Y 
A)
I only
B) II only
E)
None of the statements is true.
C) III only
D) I and III
A business evaluates a proposed venture as follows. It stands to make a profit of $10,000 with probability
3/20, to make a profit of $5000 with probability 9/20, to break even with probability 1/4, and to lose
$5000 with probability 3/20. The expected profit in dollars is
A)
1500.
B) 0.
C) 3000.
E) –1500.
D) 3250.
Use the following to answer questions 4 and 5:
A psychologist studied the number of puzzles subjects were able to solve in a five-minute period while listening to soothing music.
Let X be the number of puzzles completed successfully by a subject. The psychologist found that X had the following probability
distribution:
4.
1
2
3
4
Probability
0.2
0.4
0.3
0.1
Referring to the information above, the probability that a randomly chosen subject completes at least
three puzzles in the five-minute period while listening to soothing music is
A) 0.3.
5.
Value of X
B) 0.4.
C) 0.6.
D) 0.7.
E) 0.9.
Referring to the information above, P(X < 3) has value
A) 0.3.
B) 0.4.
C) 0.6.
D) 0.9.
E) 2.
6.
Suppose there are three balls in a box. On one of the balls is the number 1, on another is the number 2,
and on the third is the number 3. You select two balls at random and without replacement from the box
and note the two numbers observed. The sample space S consists of the three equally likely outcomes {(1,
2), (1, 3), (2, 3)}. X, the sum of the numbers on the two balls selected, has the following probability
distribution:
X
3
4
5
Probability
1/3
1/3
1/3
The probability that X is at least 4 is
A) 0.
7.
B) 1/3.
C) 9/20.
D) 2/3.
E) 1.
A random variable is
A)
a hypothetical list of the possible outcomes of a random phenomenon.
B)
any phenomenon in which outcomes are equally likely.
C)
any number that changes in a predictable way in the long run.
D)
a variable used to represent the outcome of a random phenomenon.
E)
a variable whose value is a numerical outcome associated with a random phenomenon.
Use the following to answer questions 8 and 9:
In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5, you win $1; if number of spots showing is
6, you win $4; and if the number of spots showing is 1, 2, or 3, you win nothing. Let X be the amount that you win on a single play
of the game.
8.
Referring to the information above, the expected value of X is
A) $0.
9.
B) $1.
C) $1.33.
D) $2.50.
E) $4.
Referring to the information above, the variance of X is
A) 1.
B) 1.414.
C) 3/2.
D) 2.
E) 13/6.
10. A set of 10 cards consists of five red cards and five black cards. The cards are shuffled thoroughly and I
choose one at random, observe its color, and replace it in the set. The cards are thoroughly reshuffled and
I again choose a card at random, observe its color, and replace it in the set. This is done a total of four
times. Let X be the number of red cards observed in these four trials. The mean of X is
A) 4.
B) 2.
C) 1.
D) 0.5.
E) 0.1.
11. In 1989 Newsweek reported that 60% of young children have blood lead levels that could impair their neurological
development. Assuming that a class in a school is a random sample from the population of all children at risk, the probability
that more than 3 children have to be tested until one is found to have a blood level that may impair development is
A) 0.064
B) 0.096.
C) 0.64.
D) 0.16.
E) 0.88.
12. Consider the following probability histogram for a discrete random variable X.
This probability histogram corresponds to which of the following probability distributions for X?
A)
X
P(X)
B)
X
P(X)
C)
X
P(X)
D)
E)
0
1
2
3
4
0.06
0.25
0.38
0.25
0.06
0
1
2
3
4
0.10
0.25
0.30
0.20
0.15
0
1
2
3
4
0.10
0.25
0.30
0.25
0.10
1
0.35
2
0.65
3
0.85
4
1.0
X
0
P(X)
0.10
None of the above.
13. Suppose X is a random variable with mean µX and standard deviation σX. Suppose Y is a random variable
with mean µY and standard deviation σY. The mean of X + Y is
A)
µX + µY.
B)
(µX/σX) + (µY/σY).
C)
µX
D)
(µX + µY)/(σX+σY).
E)
(µX/σX) + (µY/σY), but only if X and Y are independent.
+ µY, but only if X and Y are independent.
14. A basketball player makes 70% of her free throws. She takes 7 free throws in a game. If the shots are independent of each
other, the probability that she makes the first 5 and misses the last 2 is about
A) 0.635.
B) 0.318.
C) 0.015.
D) 0.49.
E) 0.35.
15. A basketball player makes 70% of her free throws. She takes 7 free throws in a game. If the shots are independent of each
other, the probability that she makes 5 out of the 7 shots is about
A) 0.635.
B) 0.318.
C) 0.015.
D) 0.329.
E) 0.245.
16. I toss a fair coin a large number of times. Assuming tosses are independent, which of the following is
true?
A)
Once the number of flips is large enough (usually about 10,000), the number of heads will always be
exactly half of the total number of tosses. For example, after 10,000 tosses I should have 5000 heads.
B)
The proportion of heads will be about ½, and this proportion will tend to get closer and closer to ½
as the number of tosses increases.
C)
As the number of tosses increases, any run of heads will be balanced by a corresponding run of tails
so that the overall proportion of heads is ½.
D)
If the number of heads is greater than the number of tails for the first 5000 tosses, then the number of
tails will be greater than the number of heads for the next 5000 tosses.
E)
All of the above.
Use the following to answer questions 17 through 19:
A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax from 5% to 6%, with the
additional revenue going to education. Let X denote the number in the sample that say they support the increase. Suppose that 40%
of all adults in Ohio support the increase.
17. The mean of X is
A) 5%.
B) 0.40.
C) 0.75.
D) 40.
E) 600.
18. The standard deviation of X is
A) 360.
B) 40.
C) 24.49.
D) 18.97.
E) 8.44.
19. The probability that X is more than 750 is
A) less than 0.0001.
B) about 0.1.
C) 0.3372.
D) 0.4602.
E) 0.5.
20. A fair coin (one for which both the probability of heads and the probability of tails are 0.5) is tossed
six times. The probability that less than 1/3 of the tosses are heads is
A) 0.33.
B) 0.2061.
C) 0.109.
D) 0.09.
E) 0.0043.
21. Suppose X is binomial with parameters n = 9 and p = 1/3. The probability that X is either 0 or 1 is
A) 0.6667.
B) 0.3333.
C) 0.1431.
D) 0.1111.
E) less than 0.0001.
22. Suppose X is binomial with parameters n = 6 and p = 2/3. The probability that X is at least 5 is
A) 0.6667.
B) 0.4444.
C) 0.3512.
D) 0.2634.
E) 0.0878.
23. In a test of ESP (extrasensory perception), the experimenter looks at cards that are hidden from the
subject. Each card contains a star, a circle, a wavy line, or a square. The subject tries to read the
experimenter’s mind and name the shape on each card. If the subject is just guessing, what is the
probability that it takes more than four trials before getting the first correct guess?
A) 0.250.
B) 0.316.
C) 0.422.
D) 0.500.
E) 0.684.
Use the following to answer questions 24 and 25:
There are 20 multiple-choice questions on an exam, each having possible responses a, b, c, or d. Suppose a student guesses the
answer to each question, and the guesses from question to question are independent. Let X be the number of questions for which
the student has the same answer as the person sitting next to him on his right.
24. The distribution of X is
A)
binomial with parameters n = 20 and p = 0.2.
B)
binomial with parameters n = 20 and p = 0.25.
C)
binomial with parameters n = 4 and p = 0.25.
D)
binomial with parameters n = 40 and p = 0.25.
E)
impossible to determine unless the student sitting next to him is also guessing.
25. The probability that X is zero is closest to
A) 0.0001.
B) 0.0032.
C) 0.0243.
D) 0.2373.
E) 0.3277.
26. A small class has 10 students. Five of the students are male and five are female. I write the name of each
student on a 3-by-5 card. The cards are shuffled thoroughly and I choose one at random, observe the name
of the student, and replace it in the set. The cards are thoroughly reshuffled and I again choose a card at
random, observe the name, and replace it in the set. Let X be the number of cards observed until I get one
with a name corresponding to a male student. The probability that X is greater than 1 is
A) 0.125.
1.
11. A
21. C
D
B) 0.200.
C) 0.250.
2.E
12. B
22. C
3.C
13. A
23. B
D) 0.500.
4.B
14. C
24. B
E) 0.750.
5.C
15. B
25. B
6. D
16. B
26. D
7. E
17. E
8. B
18. D
9. D
19. A
10. B
20. C