Question number 1.
Your answer was D. Correct. A manufacturer of matches randomly and independently puts 21 matches in each box of matches produced. The company knows that one-tenth of 8 percent of the matches are
flawed. What is the probability that a matchbox will have one or fewer matches with a flaw?
A
0.006813
B
0.1431
C
0.9920
D
0.9878
E
0.8448
F
None of the above
Question number 2.
Your answer was A. Correct. Let X be the number of flaws on the surface of a randomly selected boiler of a certain type and suppose X is a Poisson distributed random variable with parameter μ = 5. Find P(3 ≤
X ≤
6)
A
0.6375
B
0.6925
C
0.3624
D
0.5824
E
0.1462
F
None of the above
Question number 3.
Your answer was C. Correct. Suppose you have a distribution, X, with mean = 7 and standard deviation = 4. Define a new random variable Y = 2X - 4. Find the mean and standard deviation of Y.
A
E[Y] = 10; σ
Y
= 16
B
E[Y] = 10; σ
Y
= 4
C
E[Y] = 10; σ
Y
= 8
D
E[Y] = 14; σ
Y
= 4
E
E[Y] = 14; σ
Y
= 16
F
None of the above
Question number 4.
Your answer was C. Correct. Each year a company selects a number of employees for a management training program. On average, 20 percent of those sent complete the program. Out of the 24 people sent, what
is the probability that exactly 3 complete the program?
A
0.1933
B
0.2638
C
0.1493
D
0.3638
E
0.3493
F
None of the above
Question number 5.
Your answer was D. Correct. Each year a company selects a number of employees for a management training program. On average, 70 percent of those sent complete the program. Out of the 21 people sent, what
is the probability that 9 or more complete the program?
A
0.0087
B
0.0024
C
0.9912
D
0.9975
E
0.1087
F
None of the above
Question number 6.
Your answer was C. Correct. A fish tank in a pet store has 21 fish in it. 6 are orange and 15 are white. Determine the probability that if we select 3 fish from the tank, at least 2 will be white.
A
1.0357
B
0.2062
C
0.8157
D
0.7142
E
0.1842
F
None of the above
Question number 7.
Your answer was B. Correct. The number of people arriving for treatment at an emergency room can be modeled by a Poisson process with a mean of 7 people per hour. How many people do you expect to arrive
during a 55-minute period?
A
385.00
B
6.41
C
7.00
D
1.00
E
0.59
F
None of the above
Question number 8.
Your answer was D. Correct. Determine the type of distribution for the following situation:
Draw marbles from a bag which contains 5 red marbles, 6 blue marbles and 4 green marbles with replacement until you get a blue marble.
A
Binomial
B
Poisson
C
Hypergeometric
D
None of these
Question number 9.
Your answer was B. Correct. Suppose two random variables, and are independent, which statement is false
?
A
B
C
D
E
None of the above are false.
Question number 10.
Your answer was C. Correct. Using the joint probability table below, determine .
Y
\
X
0 1 3 0 0.15 0.05 5 0.1 0.15 0.3 7 0.05 0.05 0.15 A
0.6
B
0.75
C
0.15
D
0.25
E
0.05
F
None of the above.
Question number 11.
Your answer was B. Correct. Using the joint probability table below, determine the marginal distribution of .
Y
\
X
0 1 3 0.15 0 0.05 5 0.05 0.15 0.05 7 0.15 0.3 0.1 A
X
0 1 0.2 0.25 0.55 B
X
0 1 0.35 0.45 0.2 C
X
0 1 0.15 0 0.05 D
X
0 1 0.15 0.3 0.1 E
None of the above.
Question number 12.
Your answer was B. Correct. Using the joint probability table below, determine .
Y
\
X
0 1 3 0.1 0 0.15 5 0.05 0.05 0.05 7 0.3 0.15 0.15 A
0.05
B
0.333
C
0.025
D
0.033
E
0.25
F
None of the above.
Question number 13.
Your answer was D. Correct. Using the joint probability table below, determine .
Y
\
X
0 1 3 0 0.1 0.15 5 0.05 0.05 0.15 7 0.15 0.3 0.05 A
B
C
D
E
F
None of the above.
Question number 14.
Your answer was C. Correct. Suppose that a fair, 6 sided die is rolled. Let X
indicate the event that an odd number is rolled (in other words, X
= 1 if an odd number is rolled and X
= 0 otherwise). Let Y
indicate
the event that 2, 3, or 4 is rolled (in other words, Y
= 1 if 2, 3, or 4 is rolled and Y
= 0 otherwise). Find P
(
X
= 0, Y
= 1).
A
1
/
2
B
2
/
3
C
1
/
3
D
5
/
6
E
1
/
6
F
None of the above
Question number 15.
Your answer was B. Correct. Suppose , x
= 1, 2, 3, y
= 1, 2 is the joint pmf of X
and Y
. Determine P
(
Y
= 2).
A
5
/
6
B
3
/
5
C
1
/
6
D
1
/
3
E
1
/
2
F
None of the above
X
Y
P
(
X
∩
Y
) =
P
(
X
)
⋅
P
(
Y
)
P
(
X
∩
Y
) = 0
P
(
X
∣
Y
) =
P
(
X
)
Cov
(
X
,
Y
) = 0
P
(
X
= 1,
Y
= 7)
−
1
X
−
1
−
1
P
(
X
)
−
1
P
(
X
)
−
1
P
(
X
)
−
1
P
(
X
)
P
(
X
= 0
∣
Y
= 5)
−
1
E
(
XY
)
−
1
5.65
1.0
5.50
0.25
0.15
p
(
x
,
y
) =
x
+ 2
y
30
