Download MAT211_Final_A_Fall2014

MAT 211
Fall 2014
Instructor:
Final Exam – FORM A
Directions: There are 17 questions worth a total of 100 points.
 There are 12 multiple choice questions worth 5 points each.
Please fill in the answer grid on the last page.
 There are 5 free response questions worth 8 points each. You MUST
SHOW YOUR WORK for the free response questions. Box your
answer. Leave your answer in exact form unless otherwise noted.
Read all the questions carefully. Always indicate how a calculator was used
(i.e. sketch graph, etc. …). No calculators with QWERTY keyboards or ones
like TI-89 or TI-92 that do symbolic algebra may be used.
Honor Statement:
By signing below you confirm that you have neither given nor received any unauthorized
assistance on this exam. This includes any use of a graphing calculator beyond those uses
specifically authorized by the Mathematics Department and your instructor. Furthermore, you
agree not to discuss this exam with anyone until the exam testing period is over. In addition, your
calculator’s program memory and menus may be checked at any time and cleared by any testing
center proctor or Mathematics Department instructor.
_______________________________
Print Name
________________________________________
Signature
_____________________
Class Day and Time
_________________
Date
For problems 1 and 2: Use the following scenario:
Three fair coins are tossed, and X is the square of the number of heads showing.
1. Which is the correct histogram for the probability distribution described above.
2. Calculate P(1 ≤ X ≤ 4).
a.
1
4
b.
3
4
c.
3
8
d.
7
8
e. None of the choices.
3.
Your class is given a mathematics exam worth 100 points; X is the average score, rounded to the nearest
whole number. Classify the random variable X as finite, discrete infinite, or continuous, and indicate the
values that X can take.
a. X is discrete infinite, X is a value in the set {0, 1, 2, …, 100}
b. X is finite, X is any nonnegative value
c. X is continuous, X is a value in the set {0, 1, 2, …, 100}
d. X is finite, X is a value in the set {0, 1, 2, …, 100}
e. None of the choices
4. You are performing 7 independent Bernoulli trials with p = 0.4 and q = 0.6.
Calculate the probability rounded to four decimal places of P(X = 2).
a.
b.
c.
d.
e.
0.2613
0.0774
0.0037
0.0102
None of the choices.
5. You are performing 6 independent Bernoulli trials with p = 0.3 and q = 0.7.
Calculate the probability rounded to five decimal places of at least three successes.
a.
b.
c.
d.
e.
0.74431
0.00926
0.25569
0.18522
None of the choices.
6. The probability that a randomly selected teenager watched a rented video at least once during
a week was 0.68. What is the probability that at least 6 teenagers in a group of 8 watched a
rented movie at least once a week? Round the answer to 4 decimal places.
a. 0.2835
b. 0.5013
c. 0.0101
d. 0.0005
e. None of the choices.
7. Compute the mean, median and mode:
2, 6, 6, 10, −4
a.
b.
c.
d.
e.
Mean: 4 Median: 6
Mean: 5 Median: 6
Mean: 6 Median: 4
Mean: 4 Median: 4
None of the above.
Mode: 6
Mode: 6
Mode: 6
Mode: 6
8. Calculate the expected value of X, E(X), for the given probability distribution.
x
P(X = x)
a. 1
b. 0.8
0
0.6
1
0.1
c. 0.4
2
0.1
d. 0.9
3
0.2
e. None of the choices
9. Compute the standard deviation to 2 decimal places of the data sample.
−1, 5, 5, 8, 13
a.
b.
c.
d.
e.
10.20
4.56
5.10
26.00
None of the choices.
10. Calculate the standard deviation σ of X to 2 decimal places for the probability distribution.
x
P(X = x)
a.
b.
c.
d.
e.
1
0.2
2
0.3
3
0.3
4
0.2
2.5
1.02
0.3
1.51
None of the choices.
11. Z is the standard normal distribution. Find the indicated probability to four decimal places.
P(−0.61 ≤ Z ≤ 1.31)
a.
b.
c.
d.
0.6289
0.2291
0.1758
0.6340
e. None of the choices
12. Suppose X is a normal random variable with mean μ = 90 and standard deviation σ = 9.
Find b to one decimal places such that
P(90 ≤ X ≤ b) = 0.3.
a. 97.6
b. 125.6
c. 101.2
d. 120
e. None of the choices
FREE RESPONSE Show your work.
For numbers 1 to 3, use the following table shows the number of males in a country in 2000,
broken down by age. Numbers are in millions.
Age
0–18
18–25
25–35
35–45
45–55
55–65
65–75
Number
39.2
15.8
21.4
25.1
19.3
12.3
9.3
75
and
over
6.8
1. Construct the associated probability distribution with probabilities rounded to four decimal
places.
Age
0–18
18–25
25–35
35–45
45–55
55–65
65–75
75
and
over
Probability
2. Find P(25 ≤ X ≤ 65).
3. Find P(X ≥ 15).
4. Check whether the given function is a probability density function. If a function fails to be a
probability density function, say why.
1
f (x) = 7 - x 2 on [0, 1].
3
(
)
5. Find the value of k for which the given function is a probability density function.
f (x) = ke kx on [0, 7].
PRINT NAME: __________________________
Answer Grid:
Please fill in the correct choice using capital letters only.
1.
2.
3.
4.
5.
6.
7.
8.
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10.
11.
12.