AUXESIS REVIEW CENTER Day 3 – Engineering Data Analysis I

Regular Review Program Prepared by: Engr. John Ryan Regalario

1. Combo meals come in three dishes. One can a. 72

have a pizza, spaghetti and a burger. If there are b. 144
4 types of pizza, 3 types of spaghetti and 2 types c. 12
of burger, how many combo meals are there? d. 24
a. 24
b. 44 9. In how many ways can you arrange 3 different
c. 9 keys on a keychain?
d. 13 a. 6
b. 1
2. A, B, C and D are going to ride in A’s car to go to c. 2
the mall. But only A and C know how to drive d. 12
and D does not want to sit in front. How many
ways can the four sit on the car if the car has 10. My school's ECE club has 6 boys and 8 girls. I
two front seats and two back seats? need to select a team to send to the IECEP
a. 10 competition. We want 6 people on the team. In
b. 6 how many ways can I select the team to have 4
c. 12 girls and 2 boys?
d. 8 a. 1414
b. 1050
3. In a press conference before the All-Star Game, c. 28
eight All-Stars will be taking questions. Three d. 56
are Cubs, three are Red Sox, and two are
Yankees. If teammates insist on sitting together, 11. In how many ways can you invite one or more of
how many ways can the eight All-Stars be your five friends into your birthday party?
seated in a row? a. 25
a. 342 b. 32
b. 363 c. 31
c. 432 d. 10
d. 636
12. Find the number of ordered triples of positive
4. In how many ways can one hang 10 different integers (a, b, c) such that a + b + c = 8.
paintings on 5 empty spaces on the wall? a. 20
a. 30240 b. 21
b. 30420 c. 22
c. 32040 d. 23
d. 34020
13. Find the number of ordered quadruples of
5. In how many ways can you arrange 5 identical positive integers (a, b, c, d) such that a + b + c +
black balls, 3 identical green balls and 4 identical d = 12.
white balls in a straight line? a. 445
a. 22770 b. 450
b. 20727 c. 455
c. 72720 d. 460
d. 27720
14. Which of the following is equivalent to 15C15 +
6. How many distinct permutations do the word 16C15 + 17C15 +…+ 2023C15?
ENGINEERING has? a. 2024C15
a. 277200 b. 2023C16
b. 272700 c. 2024C16
c. 727200 d. 2023C15
d. 277020
7. 15. A survey of 500 television viewers produced the
7. There are 5 positions on a flagstaff and 4 following results: 285 watch football games, 195
different colors of flags, at least 5 flags of each watch hockey games, 115 watch basketball
color. How many different signals are possible games, 45 watch football and basketball games,
by displaying 5 flags simultaneously? Note that 70 watch football and hockey games, 50 watch
arrangement and order is important. hockey and basketball games and 50 do not
a. 120 watch any of these games. How many watch all
b. 625 of these three games?
c. 1024 a. 95
d. 20 b. 85
c. 110
8. If there are 6 persons, in how many ways can d. 20
they sit on a round table if two of them always
want to be next to each other while another 2 of 16. Bay Area rapid food sells chicken nuggets. You
them don't want to be next to one another? can buy packages of 11 or 7. What is the largest
integer n such that there is no way to buy n
nuggets?

1
AUXESIS REVIEW CENTER Day 3 – Engineering Data Analysis I
Regular Review Program Prepared by: Engr. John Ryan Regalario
a. 56 24. A point is selected at random inside a circle.
b. 57 Find the probability that the point is closer to the
c. 58 center than to its circumference.
d. 59 a. 1/4
b. 1/2
17. Persons A, B, C and D seat in four seats 1, 2, 3, c. 1/3
4 in this order. How many sitting arrangements d. 1
are there, in which no one of four persons seats
on his chair? 25. Both the bus and you get to the bus stop at
a. 7 random times between 12pm and 1pm. When
b. 8 the bus arrives, it waits for 5 minutes before
c. 9 leaving. When you arrive, you wait for 20
d. 10 minutes before leaving if the bus doesn’t come.
What is the probability that you catch the bus?
18. I have 7 pairs of socks in my drawer, one of a. 103/288
each color of the rainbow. How many socks do I b. 1/4
have to draw out in order to guarantee that I c. 47/144
have grabbed at least one pair? d. 15/16
a. 3
b. 7 26. Two red books and 4 blue books are placed at
c. 8 random on a shelf. What is the probability that
d. 13 the blue books will be together?
a. 0.1
19. A bag has 4 red marbles, 5 white marbles, and 6 b. 0.143
blue marbles. Three marbles are drawn from the c. 0.2
bag (without replacement). What is the d. 0.341
probability that they are all the same color?
a. 34/455 27. Suppose all 6 men at a party throw their hats in
b. 17/455 the center of the room. Each man then randomly
c. 43/455 selects a hat. Find the probability that none of
d. 71/455 the 6 men selects his own hat.
a. 25/72
20. Pikachu tries to solve a really hard problem once b. 17/48
each day. He has a 1/4 probability of solving it c. 13/36
each day. What is the probability that he will d. 53/144
solve it before his sixth try?
a. 0.763 28. What is the probability of getting a 9 exactly
b. 0.367 once in three throws of a pair of dice?
c. 0.237 a. 0.561
d. 0.732 b. 0.263
c. 0.862
21. Pikachu, Mudkip and Cyndaquill have different d. 0.751
chances of hitting the target. Pikachu can hit the
target 3/4 of the time, Mudkip can hit the target 29. What is the probability that exactly 2 out of 3
2/3 of the time and Cyndaquill can hit the target tosses of a fair coin will be heads?
1/2 of the time. They all go for the target a. 1/4
simultaneously. What is the probability that at b. 1/2
least one of them will hit the target? c. 3/8
a. 23/24 d. 5/8
b. ¼
c. 1/24 30. Four light bulbs are chosen at random from 20
d. 3/4 bulbs of which 5 are defective. Find the
probability that exactly one is defective.
22. What is the probability of drawing either an ace a. 0.2787
or a king in a single draw from a deck of 52 b. 0.0493
playing cards? c. 0.1897
a. 1/13 d. 0.4696
b. 7/52
c. 2/13 31. What is the probability that of 5 cards dealt from
d. 1/6 a well – shuffled deck, 3 will be hearts and two
spades?
23. Two people are chosen randomly from 4 married a. 143/16660
couples. What is the probability that they are b. 29/4560
husband and wife? c. 253/16660
a. 1/28 d. 43/4560
b. 3/28
c. 1/14 32. Most graduate schools of business require
d. 1/7 applicants for admission to take the Graduate
Management Admission Council’s GMAT
examination. Scores on the GMAT are roughly
2
AUXESIS REVIEW CENTER Day 3 – Engineering Data Analysis I
Regular Review Program Prepared by: Engr. John Ryan Regalario
normally distributed with a mean of 527 and a a. 1/2
standard deviation of 112. What is the probability b. 1/3
of an individual scoring above 500 on the c. 1/4
GMAT? d. 1/5
a. 0.5714
b. 0.5803 39. A pair of fair dice is thrown. Find the probability
c. 0.5953 that the sum is 10 or greater if 5 appears on at
d. 0.6006 least one of the die.
a. 1/3
33. The average number of acres burned by forest b. 1/12
and range fires in a large New Mexico county is c. 1/2
4,300 acres per year, with a standard deviation d. 3/11
of 750 acres. The distribution of the number of
acres burned is normal. What is the probability 40. In a certain college, 4% of the men and 1% of
that between 2,500 and 4,200 acres will be the women are taller than 6 feet. Furthermore,
burned in any given year? 60% of the students are women. Now if a
a. 0.4388 student is selected at random and is taller than 6
b. 0.4499 feet, what is the probability that the student is a
c. 0.4545 woman?
d. 0.4662 a. 2/11
b. 3/11
34. The Edwards’s Theater chain has studied its c. 4/11
movie customers to determine how much money d. 1/11
they spend on concessions. The study revealed
that the spending distribution is approximately 41. Suppose a voter poll is taken in three states. In
normally distributed with a mean of $4.11 and a state A, 50% of voters support the liberal
standard deviation of $1.37. What percentage of candidate, in state B, 60% of the voters support
customers will spend less than $3.00 on the liberal candidate, and in state C, 35% of the
concessions? voters support the liberal candidate. Of the total
a. 19.73% population of the three states, 40% live in state
b. 20.89% A, 25% live in state B, and 35% live in state C.
c. 21.18% Given that a voter supports the liberal candidate,
d. 22.56% what is the probability that she lives in state B?
a. 20/63
SITUATION 1 b. 10/31
The number of cars passing a point on a road c. 10/21
may be modelled by Poisson distribution. At an d. 22/63
average, 4 cars enters the Caibaan Diversion
Road in Tacloban City every 5 minutes. 42. You draw one card from a standard deck of
playing cards. If you pick a heart, you will win
35. Find the probability that in a 5-minute period two $10. If you pick a face card, which is not a heart,
cars go past you win $8. If you pick any other card, you lose
a. 0.038 $6. How much is your expected earnings?
b. 0.146 a. $0.42
c. 0.238 b. -$0.42
d. 0.382 c. $0.24
d. -$0.24
36. Find the probability that in a 5-minute period
fewer than 3 cars go past. 43. A detective figures that he has a one in nine
a. 0.038 chance of recovering stolen property. His out-of-
b. 0.146 pockets expenses for the investigation are
c. 0.238 $9,000. If he is paid his fee only if he recovers
d. 0.382 the stolen property, what should he charge
clients in order to breakeven?
37. In a class of 28 students, the teacher selects a. $108,000
four people at random to participate in a b. $90,000
geography contest. What is the probability that c. $81,000
this group of four students includes at least two d. $117,000
of the top three geography students in the class?
Express your answer as a common fraction.
a. 37/819
b. 73/918
c. 73/819
d. 37/918

38. A couple has two children. Find the probability p

that both children are boys if it is given that at
least one of the children is a boy.

3
AUXESIS REVIEW CENTER Day 3 – Engineering Data Analysis II
Regular Review Program Prepared by: Engr. John Ryan Regalario

1. Find the median of the following scores: 30, 11. Find the value of the third quartile.
73, 62, 60, 58, 70, 60, 95, 66, 51, 85. a. 43 c. 45
a. 62 c. 30 b. 44 d. 46
b. 60 d. 70
12. Find the value of the interquartile range.
2. Find the median of the following scores: 73, a. 18 c. 20
62, 60, 58, 70, 60, 90, 66, 51, 85. b. 19 d. 21
a. 66 c. 60
b. 62 d. 64 13. An English class consists of 20 French
students, 25 Italian students and 15
3. On the first six tests, Pikachu’s scores were Spanish students. On an exam, the French
95, 91, 92, 78, 92 and 86. If Pikachu took a students averaged 78, Italian students
seventh test and raised his tests’ mean by averaged 75 and Spanish students average
exactly +1, what was his score on the 76. Find the mean grade of the class.
seventh test?
a. 89 c. 95 a. 76 c. 76.25
b. 92 d. 96 b. 76.75 d. 76.65

4. During the given month, ten farmers sold SITUATION 2

13, 17, 10, 18, 18, 9, 17, 13, 15, 14 sacks of Given the following data: 80, 90, 100
rice respectively. What is the mode of this
group of data? 14. Evaluate the value of the mean.
a. 13 c. 18 a. 80 c. 95
b. 17 d. all of the choices b. 90 d. 100

5. During the given month, ten farmers sold 15. Evaluate the value of the population
13, 17, 10, 18, 18, 9, 17, 13, 15, 14 sacks of standard deviation.
rice respectively. Determine the midrange. a. 8.16 c. 11.16
a. 4.5 c. 13.5 b. 10 d. 13
b. 9 d. 18
16. What is the value of the coefficient of
6. Find the mean deviation of the following variation?
scores: 5, 4, 6, 8, 7, 9, 5, 3, 6, 8. a. 81.84 c. 734.85
a. 3.12 c. 2.11 b. 98.16 d. 9.07%
b. 1.52 d. 4.25
SITUATION 3
7. Ryan gets 50 on his Statistics midterm The ratings of the successful examinees
where the mean of his class is 40 and the who garnered the top ten highest places in
standard deviation is 10. Determine his z- the November 2017 Chemical Engineer
score. Licensure Examination are as follows:
a. -1 c. 1 {84.60, 84.60, 83.90, 83.90, 83.70, 83.60,
b. 0 d. 5 83.40, 83.40, 83.30, 83.30, 83.00, 82.80,
82.50, 82.50, 82.40}
8. Find the quadratic mean of the numbers 3,
5, 6, 6, 7, 10 and 12. 17. What is the geometric mean of the ratings?
a. 7.0 c. 7.55 a. 83.40 c. 83.47
b. 7.25 d. 7.85 b. 83.32 d. 83.39

9. Find the standard deviation of the following 18. What is the population standard deviation?
data 2, 5, 3, 4, 7, 0, 11, 2, 3, 8. a. 0.6446 c. 0.6902
a. 3.1 c. 3.5 b. 0.6347 d. 0.6668
b. 3.3 d. 3.7
19. What is the population variance?
SITUATION 1 a. 0.4446 c. 0.4672
Given the following set of data: b. 0.4462 d. 0.4764
25, 32, 49, 21, 37, 43, 27, 45, 3

10. Find the value of the first quartile.

a. 25 c. 27
b. 26 d. 28

4
AUXESIS REVIEW CENTER Day 3 – Engineering Data Analysis II
Regular Review Program Prepared by: Engr. John Ryan Regalario

20. The marks obtained in English test by 17 26. Suppose we wish to test H0:   53 vs Ha: 
students were recorded. What is the median > 53. What will result if we conclude that the
marks of the students? mean is greater than 53 when its true value
Marks Frequency is really 55?
0-10 2 a. we have made a type I error
10-20 4 b. we have made a correct decision
20-30 5 c. we have made a type II error
30-40 4 d. none of the above are correct
40-50 2
a. 22 c. 24 27. A hypothesis test is used to prevent a
b. 23 d. 25 machine from underfilling or overfilling quart
bottles of beer. On the basis of sample, the
21. The heights, in cm, of 50 students are machine is shut down for inspection. A
recorded below. What is the modal height? thorough examination reveals there is
Height No. of Students nothing wrong with the filling machine. From
125-130 7 a statistical point of view:
130-135 14 a. both type I and type II errors were made
135-140 10 b. type I error was made
140-145 10 c. type II error was made
d. a correct decision was made
145-150 9
a. 133.18 c. 135.04
b. 134.26 d. 136.68 28. Suppose we wish to test H0:   21 vs Ha: 
< 21. Which of the following possible
22. Suppose you could take all samples of size sample results gives the most evidence to
64 from a population with a mean of 12 and support Ha?
a standard deviation of 3.2. What would be a. x̅ = 23, s = 3
the standard deviation of the sample b. x̅ = 19, s = 4
means? c. x̅ = 17, s = 7
a. 3.2 c. 0.4 d. x̅ = 18, s = 6
b. 0.2 d. 0.3
SITUATION 4 29. Given H0:  = 25, Ha:   25, and P-value =
The uniform distribution on the interval [0, 1] 0.041. Do you reject or fail to reject H0 at
has the probability density function the 0.01 level of significance?
0 if x < 0 or x > 1 a. fail to reject H0
f(x) = { b. not sufficient information to decide
1 if 0 ≤ x ≤ 1
Letting X be the associated random c. reject H0
variable,
30. If a hypothesis test were conducted using 
23. Compute E(X). = 0.05, for which of the following p-values
a. 1/2 c. 1/4 would the null hypothesis be rejected?
b. 1/3 d. 1/12 a. 0.100 c. 0.055
b. 0.041 d. 0.060
24. Compute Var(X).
a. 1/2 c. 1/4 31. The scores for nine students in history and
b. 1/3 d. 1/12 algebra are as follows:
History: 35, 23, 47, 17, 10, 43, 9, 6, 28
25. The owner of travel agency would like to Algebra: 30, 33, 45, 23, 8, 49, 12, 4, 31
determine whether or not the mean age of Compute the Spearman rank correlation.
the agency’s customers is over 24. If so, he a. 0.6 c. 0.8
plans to alter the destination of their special b. 0.7 d. 0.9
cruises and tours. If he concludes the mean
age is over 24 when it is not, he makes a 32. Calculate the coefficient of rank correlation
_________ error. If he concludes the mean of the scores obtained by 7 students in an
age is not over 24 when it is, he makes essay writing competition by two judges, X
________ error. and Y.
a. type II, type II c. type I, type II X: 15, 12, 20, 16, 18, 20, 26
b. type I, type I d. type II, type I Y: 10, 15, 11, 11, 25, 18, 30

a. 0.25 c. 0.5625
b. 0.4375 d. 0.75

5
AUXESIS REVIEW CENTER Day 3 – Engineering Data Analysis II
Regular Review Program Prepared by: Engr. John Ryan Regalario

Complete the ANOVA table

Source Sum of Degrees Mean F

Squares of Squares
Freedom
Treatments SST DFT MST F
Errors SSE DFE MSE

The data below resulted from measuring the

difference in resistance resulting from
subjecting identical resistors to three
different temperatures for a period of 24
hours. The sample size of each group was 5.
In the language of design of experiments, we
have an experiment in which each of three
treatments was replicated 5 times

Level 1 Level 2 Level 3

6.9 8.3 8.0
5.4 6.8 10.5
5.8 7.8 8.1
4.6 9.2 6.9
4.0 6.5 9.3
Means

33. What is the value of SST (Sum of Squares

between Treatments)?
a. 24.902 c. 26.634
b. 25.681 d. 27.897

34. What is the value of SSE (Sum of Squares

of Errors)?
a. 17.452 c. 19.214
b. 18.012 d. 20.675

35. What is the value of DFT (Degrees of

Freedom between Treatments)?
a. 1 c. 3
b. 2 d. 4

36. What is the value of DFE (Degrees of

Freedom of Errors)?
a. 11 c. 13
b. 12 d. 14

37. E valuate the F value.

a. 7.76 c. 9.59
b. 8.35 d. 10.12