Download AP Statistics - Chapter 4B Extra Practice

AP Statistics - Chapter 4B Extra Practice
Let the random variable X be a random number with the uniform density curve given.
3. Referring to the information above, P(X = 0.25) is
A) 0.00
B) 0.25
C) 0.75
D) 1.00
4. Referring to the information above, P(X  0) has value
A) 0.0
B) 0.1
C) 0.5
D) 1.0
5. Referring to the information above, P(0.7 < X < 1.1) has value
A) 0.30
B) 0.40
C) 0.60
D) 0.70
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 4. 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
total of the two balls selected, has probabilities
X
3
4
5
Probability
1/3
1/3
1/3
The probability that X is at least 4 is
A) 0
B) 1/3
C) 2/ 3
D) 1.0
10.
A)
B)
C)
D)
A random variable is
a hypothetical list of the possible outcomes of a random phenomenon
any phenomenon in which outcomes are equally likely
any number that changes in a predictable way in the long run
a variable whose value is a numerical outcome of a random phenomenon
12. The probability histogram for a random variable X corresponds to which of the following distributions for X?
A) X
0
1
P(X)
0.06
0.25
B) X
0
1
P(X)
0.10
0.25
C) X
0
1
P(X)
0.10
0.25
D) None of the above
2
0.38
2
0.30
2
0.30
3
0.25
3
0.20
3
0.25
4
0.06
4
0.15
4
0.10
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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)}. Let X be the total of the two balls selected.
17. Referring to the information above, the mean of X is
A) 2.0
B) 14/6
C) 4.0
D) 26/6
18. Referring to the information above, the variance of X is
A) 1/3
B) 2/3
C) 1
D) 4
19. In a particular game, a ball is randomly chosen from a box that contains three red balls, one green ball, and six blue
balls. If a red ball is selected you win $2, if a green ball is selected you win $4, and if a blue ball is selected you
win nothing. Let X be the amount that you win. The expected value of X is
A) $1
B) $2
C) $3
D) $4
26. A random variable X has mean X and standard deviation X. Suppose n independent observations of X are taken
and the average J of these n observations is computed. If n is very large, the law of large numbers implies
A) that J will be close to X
B) that J will be approximately normally distributed
C) that the standard deviation of J will be close to X
D) all of the above
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.
Value of X
Probability
1
0.2
2
0.4
3
0.3
4
0.1
31. Referring to the information above, the mean number of puzzles completed successfully, X, is
A) 1
B) 2
C) 2.3
D) 2.5
32. Referring to the information above, if three subjects solve puzzles for five minutes each and the number of puzzles
solved by each subject is independent of each other, then the mean of the total number of puzzles solved by the
three subjects is
A) 2.3
B) 2.5
C) 6.9
D) 7.5
33. I roll a fair die and count the number of spots on the upward face. A fair die is one for which each of the outcomes
1, 2, 3, 4, 5, and 6 are equally likely. According to the law of large numbers
A) several (four or five) consecutive rolls for which the outcome 1 is observed is impossible in the long run. If such an
event did occur, it would mean the die is no longer fair
B) after rolling a 1, you will usually roll nearly all the numbers at least once before rolling a 1 again
C) in the long run, a 1 will be observed about every sixth roll and certainly at least once in every 8 or 9 rolls
D) none of the above is true
The weight of medium-size tomatoes selected at random from a bin at the local supermarket is a normal random variable with
mean  = 10 ounces and standard deviation  = 1 ounce. Suppose we pick two tomatoes at random from the bin, so the
weights of the tomatoes are independent.
37. Referring to the information above, the difference in the weights of the two tomatoes selected (the weight of first
tomato minus the weight of the second tomato) is a random variable with which distribution?
A) N(0, 0.5)
B) N(0, 1.41)
C) N(0, 2)
D) uniform with mean 0
38. Referring to the information above, the probability that the difference in the weights of the two tomatoes exceeds 2
ounces is
A) 0.0170
B) 0.0340
C) 0.0680
D) 0.1587
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Answer Key
3.
4.
5.
6.
10.
12.
17.
18.
19.
26.
31.
32.
33.
37.
38.
A
A
A
C
D
B
C
B
A
A
C
C
D
B
B
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