MATH 166 Exam II Sample Questions
Use the histogram below to answer Questions 1-2:
(NOTE: All heights are multiples of .05)
1. What is P (X ≥ 1)?
(a) 0.00525
(b) 0.0525
(c) 0.4
(d) 0.5
(e) 0.6
2. What is E(X)?
(a) 0.7
(b) 0.9
(c) 1.5
(d) 2.0
(e) 3.0
3. A password must contain 6 to 8 characters consisting of lowercase letters a-z, capital letters A-Z, and digits 0-9.
How many passwords are possible if the first character must be a (capital or lowercase) letter and characters are
not allowed to be repeated? (NOTE: “a” is different from “A”).
(a) 1.891 × 1014
(b) 1.363 × 1014
(c) 1.289 × 1014
(d) 1.185 × 1014
(e) None of these
4. In how many different ways can eight Pokemon line up if Pikachu and Dedenne must be together and Squirtle,
Bulbasaur, and Charizard must be together?
(a) 40,320
(b) 120
(c) 512
(d) 1,440
(e) 3,360
5. How many different arrangements of the word REVEILLE are possible?
(a) 120
(b) 512
(c) 1,440
(d) 3,360
(e) 40,320
6. In planning next semester’s schedule you have to choose one of three possible math courses, one of four
HIST/POLS courses, two of four science courses, and one of six kinesiology courses (for relaxation). How
many different curricula are available for consideration? Ignore times, rooms, instructors, etc.
(a) 432
(b) 864
(c) 6,188
(d) 10,296
(e) 103,680
7. A medical student knows 80 of the 100 diseases covered on the midterm. If 50 diseases are put on the exam,
what is the probability that the student knows exactly 40 of them?
(a) 1.066 × 10−6
(b) 1.917 × 10−11
(c) 0.1398
(d) 0.1969
(e) 0.8000
8. Which of the histograms below has the largest variance:
(I)
0.5
0.5
0.5
0.45
0.45
0.45
0.4
0.4
0.4
0.35
0.35
0.35
0.3
0.3
0.3
0.25
0.25
0.25
0.2
0.2
0.2
0.15
0.15
0.15
0.1
0.1
0.1
0.05
0.05
0.05
0
-1
-0.5
0
0.5
1
1.5
2
(a) I
(b) II
(c) III
(d) I and III
(e) all are equal
2.5
3
3.5
4
(II)
0
-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
(III)
0
-1
-0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
9. A new drug is found to cause side effects in 35% of the people who take the drug. If 400 people take the drug,
what is the mean and standard deviation (to two decimal places) of the number of people who will experience
side effects?
(a) µ = 140, σ = 91.00
(b) µ = 260, σ = 9.54
(c) µ = 140, σ = 11.83
(d) µ = 260, σ = 11.83
(e) µ = 140, σ = 9.54
10. An employer provides an annual insurance policy which covers against death and against disability. The policy
pays $40,000 if the employee is disabled and $200,000 in the event of the employees death. The probabilities of
these events happening in the next year are 0.002 and 0.0008, respectively. What is the minimum the employer
should charge for this policy?
(a) $160
(b) $240
(c) $432
(d) $857
(e) $1200
11. Given a bag of 75 M&Ms, 10 of which are green, consider the following random variables:
Let X1 be the number of M&Ms drawn from the bag, without replacement, until you get a green one.
Let X2 be the number of M&Ms drawn from the bag, with replacement, until you get a green one.
Which statement below is true?
(a) X1 is finite discrete and X2 is infinite discrete.
(b) X1 is infinite discrete and X2 is finite discrete.
(c) Both X1 and X2 are finite discrete.
(d) Both X1 and X2 are infinite discrete.
(e) None of these is true.
12. Eleven players of the US Women’s National soccer team are to travel together to a charity dinner in a seven-seater
SUV and a 4-seater sports car. How many different seating arrangements are possible if only Alex Morgan, Hope
Solo, and Abby Wambach are willing to drive and the others don’t care where they sit as long as they are not
driving?
(a) 2,177,280
(b) 1,088,640
(c) 483,840
(d) 6,652,800
(e) 39,916,800
13. A medical student creates 100 notecards about the diseases covered on the midterm. While studying, they draw
a notecard at random, try to identify the disease, and replace the notecard in the pile, repeating this 50 times.
If the student knows 80 of the diseases on the notecards, what is the probability that they will get exactly 40
correct?
(a) 1.066 × 10−6
(b) 1.917 × 10−11
(c) 0.1398
(d) 0.1969
(e) 0.8000
14. The probability distribution of the number of chocolate chips in a cookie is shown below:
x
4
5
6
7
8
P (X = x) 0.08 0.12 0.24 0.37 0.19
Find each of the following:
(a) Mean:
(b) Median:
(c) Mode:
(d) Variance:
(e) Standard Deviation:
15. A fair coin is tossed 3 times. Let X = the number of heads. Find the probability distribution of X.
16. Suppose 85% of all Aggies are football fans. If you survey 100 Aggies...
(a) ...what is the probability that exactly 20 are NOT football fans?
(b) ...what is the probability that at least 75 are football fans?
(c) ...what is the probability that at least 71 but fewer than 86 are football fans?
17. The US Senate consists of 54 Republicans and 46 Democrats.
(a) If a committee of 9 Senators is chosen at random, what is the probability that it contains exactly 5
Republican and 4 Democratic Senators?
(b) If a committee of 9 Senators is chosen at random, what is the probability that it contains at least one
Republican?
18. Eight baseball players, seven football players, and six basketball players apply to be on an intersport competition.
Ten players are to be chosen for the competition.
(a) In how many ways can exactly four baseball and four football players be chosen for the competition?
(b) In how many ways can exactly two football players OR exactly five basketball players be chosen for the
competition?
19. The amount of time it took to complete Exam I was normally distributed with a mean of 61 minutes and a
standard deviation of 10.4 minutes. A student who took the exam is chosen at random.
(a) What is the probability the student finished in less than 75 minutes?
(b) What is the probability the student finished between 55 and 70 minutes?
(c) If you finished before 90% of the class, how many minutes did it take you to complete the exam?
20. A carnival offers a game where the player pays $2 and then selects two marbles from a bucket containing 52
marbles, 4 of which are green. If the player draws two green marbles, they win $100. If they draw one green
marble, they win $10. Otherwise, they win nothing. Let X =the player’s net winnings. Find the probability
distribution of X.
21. Scientists estimate that 57% of all men in their 40s have noticeable hair loss. If 300 men are selected at random,
what is the probability that at least 100 but fewer than 130 do NOT have noticeable hair loss?