Exam Specifications
Mathematics
Engineering Probability and Statistics
Chemistry
Computers
Ethics and Business Practices
Engineering Economics
Statics and Dynamics
Strength of Materials
Material Properties
Fluid Mechanics
Electricity and Magnetism
Thermodynamics
15%
7%
9%
7%
7%
8%
10%
7%
7%
7%
9%
7%
BEGINNING OF
PROBABILITY AND STATISTICS
Problem 20
TOPIC:
Probability and Statistics (page 40)
Please calculate the mean, median, and mode of the following data:
1,1,3,4,1,2,1,3,4,5,5,6,1
(a) mean
(b) median
(c) mode
Problem 21
TOPIC:
Probability and Statistics (page 40)
Please calculate the variance, standard deviation and geometric mean
of the following data:
1,1,3,4,1,2,1,3,4,5,5,6,1
(a) variance
(b) standard deviation
(c) geometric mean
Problem 22
TOPIC:
Probability and Statistics (page 40)
An engineering contractor has a staff of 10 engineers, all equally qualified.
For a particular assignment 3 engineers are required.
(a) Calculate the number of permutations of engineers that could
be assigned to the work.
(b) Calculate the number of combinations of engineers that could
be assigned to the work.
Problem 23
TOPIC:
Probability and Statistics (page 41)
An assembly plant operates three lines with the following production data:
Line
A
B
C
% production
50
35
15
fraction defective
0.02
0.015
0.04
(a)Assuming that you have a defective item, what is the probability that it
was produced by line C?
(b) What is the probability of having a defective item?
Problem 24
TOPIC:
B
A
2
5
1
Probability and Statistics (page 40)
8
3
C
9
4 10 7
11
6
D
Please find the following
(a) Find A  B
(c) Find (A  B)  C
(b) Find A  B
(d) Find A  B  C  D
(e) Find (A  B)  (C  D)
(f) Find B  C
(g) Find A  B
(h) Find A  B
(i) Find A  B  D
(j) Find A  B  D
Problem 25
TOPIC:
Probability and Statistics (page 40)
A petrochemical plant makes the following breakdown of products with the
data based on a carbon balance:
Carbon Number
1-2
3-4
5-7
8-12
>12
% produced
35
35
12
9
9
Please find the following probabilities:
(a) Probability of producing products with a carbon number greater than 4
(b) Probability of producing products with a carbon number greater than 4
and less than 13
(c) Probability of producing products with a carbon number less than 13
(d) Probability of producing products with a carbon number greater than 7
Problem 26
TOPIC:
Probability and Statistics (page 41)
Please find the following cumulative distribution functions F(x) given the
probability density functions, f(x):
(a)
f ( x)  x; with 0  x  2
(b)
f ( x)  x 2 ; with 0  x  3 3
(c)
f ( x)  x; with 0  x  2
(d) Please find the mean value of the function in part (a)
Problem 27
TOPIC:
Probability and Statistics (page 42-46)
A set of ethylene yield data are normally distributed with mean of 24.7 and a
variance of 5; that is Y~N(24.7,5)
(a) Find the probability that the yield is less than 24.
(b) Find the probability that the yield is greater than 26
(c) Find the probability that the yield is between 25 and 26.
(d) Find a 95% confidence interval for this yield data assuming that 25 data
points have been taken.
(e) Find a 95% confidence interval assuming that the variance is not known
but that the sample size is 25 and the mean is 24.7 and the sample variance
is 5.
Problem 27
TOPIC:
Probability and Statistics (page 226)
A set of ethylene yield data are collected; 24.1, 25.1, 24.3, 24.6, 24.9
(a) Find the sample mean and sample variance
(b) Find the 95% confidence interval for the data.
(c) Test the hypothesis that the yield is greater than 24.5. Use a 5%
probability of a type I error
Problem 28
TOPIC:
Probability and Statistics (page 42)
(a) A salesman has a 10% chance of success on any given sales call. What is
the probability of 3 successes in 5 calls. The data are binomially
distributed.
(b) A salesman has a 10% chance of success on any given sales call. What is
the probability of 1 successes in 10 calls. The data are binomially
distributed.
(c) A salesman has a 10% chance of success on any given sales call. About
how many calls will the salesman have to make in order to have a 50%
chance of making a sale (that is, being successful).
END OF
PROBABILITY AND STATISTICS
BEGINNING OF
STATICS AND DYNAMICS
Problem 29
TOPIC:
Statics (page 49)
A = 2k m
C = 4i m
B=5j m
(a) What is the length of the vector A+B+C, the sum of the 3 orthogonal vectors.
(b) If the A vector is unknown and the length of the vector A+B+C, is 20 m,
what is the length of the A vector?
(c) f the magnitude of all the vectors are unknown yet the length of
the vector A+B+C is 20 m and A has a magnitude of twice that of B which
is twice that of C, what is the length of the A vector?
Problem 30
2300 N
TOPIC:
Statics (page 49)
C
A
3m
4m
B
(a) What is the approximate vertical force component in member BC?
(b) What is the approximate vertical force component in member AC?
Problem 31
TOPIC:
Statics (page 49)
Problem 32
TOPIC:
Statics (page 49)
Problem 33
TOPIC:
Statics (page 49)
Problem 34
TOPIC:
Statics (page 49)
Problem 35
TOPIC:
Statics (page 49)
Problem 36
TOPIC:
Statics (page 49)
Problem 37
TOPIC:
Statics (page 49)
Problem 38
TOPIC:
Statics (page 49)
Problem 39
TOPIC:
Statics (page 49)
Problem 40
TOPIC:
Statics (page 49)
Centroid
• the word centroid means the geometric
center of the object's shape.
• Informally, the center of mass (and center of
gravity in a uniform gravitational field) is the
average of all points, weighted by the local
density or specific weight.
• If a physical object has uniform density, then
its center of mass is the same as the centroid
of its shape.
Problem 41
TOPIC:
Statics (page 53)
Identify the centroid of
the following shapes
a
b
b
a = 0.5 m
b = 0.25 m
Problem 42
TOPIC:
Statics (page 53)
Identify the centroid of
the following shape
a
b
a = 0.5 m
b = 1.5 m
h = 1.25 m
Problem 43
TOPIC:
Dynamics (page 51)
Problem 43
TOPIC:
Dynamics (page 51)
Problem 44
TOPIC:
Dynamics (page 51)
Problem 45
TOPIC:
Dynamics (page 54)
Problem 46
TOPIC:
Dynamics (page 56)
What is the acceleration of
the 50 kg mass?
Assume friction;less and mass less
pulley system
Problem 47
TOPIC:
Dynamics (page 56)
Problem 48
TOPIC:
Dynamics (page 56)
Problem 49
TOPIC:
Dynamics (page 56)
Two identical balls collide along their
centerlines in an elastic collision.
The initial velocity of ball 1 is 0.85 m/s. The
initial velocity of ball 2 is –0.53 m/s.
What is the relative velocity of each ball after
the collision?
Problem 50
TOPIC:
Dynamics (page 56)
Problem 50
TOPIC:
Dynamics (page 56)
Problem 51
TOPIC:
Dynamics (page 56)
Perfectly Inelastic Collision
Problem 52
TOPIC:
Dynamics (page 56)
Problem 53
TOPIC:
Dynamics (page 56)
A snowmobile tows a sled with a weight of 3000
N. It accelerates up a 15° slope at 0.9 m/s2. The
coefficient of friction between the sled and the
snow is 0.1. What is the tension in the tow rope?
Problem 54
TOPIC:
Dynamics (page 56)
Problem 55
TOPIC:
Dynamics (page 56)
Problem 56
TOPIC:
Dynamics (page 56)
Problem 56
TOPIC:
Dynamics (page 56)
Problem 57
TOPIC:
Dynamics (page 56)
END OF
STATICS AND DYNAMICS