### Statistics and Probability Part 1: Mechanical Engineer Board Exam Review

Here are some review questions in Mathematics, Statistics and Probability.

Mechanical Engineering Board Exam Review: Statistics and Probability part 1

1. In how many ways can you arrange a group of 5 girls and 3 boys in 7 vacant chairs?
a. 40320
b. 5040
c. 720
d. 8

2. How many 3-digit numbers can you make out of the numbers 1 to 5 without repetition?
a. 720
b. 10
c. 60
d. 120

3. There are 2 white, 3 red, and 4 blue balls inside a basket. If three balls are drawn randomly in succession without replacement, what is the probability that the first ball is white, and the next two balls are blue?
a. 32/729
b. 4/63
c. 8/243
d. 1/21

4. What is the mode of the following numbers: 54, 45, 75, 60, 65, 65, 60, and 57?
a. 65
b. 60
c. 62.5
d. 60 and 65

5. From the given numbers of question number 4, what is the median?
a. 65
b. 60
c. 62.5
d. 60 and 65

6. From the given numbers of question number 4, what is the variance?
a. 77.84
b. 60.125
c. 68.11
d. 8.82

7. Seven boys are to be seated around a circular table. How many arrangements can be made?
a. 7
b. 2520
c. 5040
d. 720

8. In how many ways can you arrange 3 boys and 4 girls in a 7-seater bench supposing that the four girls want to be seated together?
a. 24
b. 5040
c. 576
d. 48

9. The probability that you will arrive late is 35% and the probability that you will scolded by your boss is 15%. What is the probability that you will be both late and scolded by your boss?
a. 5.25%
b. 50%
c. 44.75%
d. 2.33%

10. From question number 9, what is the probability that you will either be late or scolded by your boss?
a. 5.25%
b. 50%
c. 44.75%
d. 2.33%

NOTE:
If you noticed a question with no correct answer in the option or the question itself seems to be erroneous, I would appreciate if you can send me an email or comment below. Computation-type review questions are very hard to do and requires extensive validation. I would appreciate any help for the improvement of this blog. Thanks!

Answers will be posted after a week.

### BOARD EXAM TIP: Which Review Center?

First of all, I would like to apologize for a long time I haven't posted anything but introduction. The reason for that is I'm busy optimizing the design of this site. I'm hoping that the make over is good. Anyway, I would like to dedicate this article to those who are going to take/retake the board exam this coming October. My sincere wish that you bring out the best among yourselves and may the deserving ones pass the exam.

Going back to the One-Million-Peso worth question: "Which review center should I enroll?", I would like to answer that in the most unbiased way I can. Of course, I'm only human and I had also my preferences but I will try my best to hide it.

To start with I will enumerate some of the prominent review centers that offer board exam reviews for mechanical engineering in the Philippines.

1. Alcorcon (Cebu & Manila)
2. Excel (Cebu & Manila)
3. Linx Engineering (Manila)
4. MERIT (Manila)
5. PRIME (Cebu)
6. RLB's CDTC (Manila)
I'…

### PAST MECHANICAL BOARD EXAM QUESTION: Machine Design Set-1 (solutions and answers)

The following are the solutions and answers to MODIFIED PAST MECHANICAL BOARD EXAM QUESTION: Machine Design Set-1 posted on this blog last Saturday, November 14, 2009.

Again, I want to stress out that most of the questions here are modified from its original form for the purpose of improving the question.

Past Mechanical Engineering Board Exam Question Number 1
A 4 inches diameter short shaft carrying 2 pulleys close to the bearings transmits how much horsepower if the shaft makes 120 rpm.

A.200HP               B. 199 HP

C.198 HP              D. 202 HP

P = (D3N )/38 -- for mula for short shafts from PSME code

P = (4)3(120)/38

P= 202 HP

Past Mechanical Engineering Board Exam Question Number 2
An instrument that measures the hardness of the work piece in terms of elasticity.

a. Durometer

b. Scleroscope

c. Mohs's Scale

d. Brinell Tester

Source: Machinery’s Handbook

### SOLUTION TO MECHANICAL BOARD EXAM PROBLEMS: Power Set-1

Here are the solutions to board problems given at Power Subject Set-1. If you do not understand anything, feel free to write a comment voicing out your concern. I'm still looking for better ways to present my solution. I still don't know how to present equations and mathematical symbols with blogger. Please bear with me.

1. An automobile tire is inflated to 32psig pressure at 50 degree F. After being driven, the temperature rises to 75 degree F. Determine the final gage pressure assuming the volume remains constant. (Electrical Engineering Board Exam Problem)

Solution:
Since volume is constant, use Charles’ Law on constant volume processes.
P1/T1=P2/T2
Note: P and T should be absolute.

(32+14.7)/ (50+460) =P2/ (75+460)

P2=48.99 psia

Converting back to gage pressure,

P2g=48.99-14.7

P2g=34.29 psig

2. Four hundred cubic centimeters of gas at a pressure of 740 mmHg absolute and temperature of 18 degree C undergoes a process until the pressure and temperature becomes 760 mmHg abso…