City University of Hong Kong
MA3001 Niidterm Test #2
Semester B. 2015/2016
Nan :0:
ID:
I 0.5110115! Total Marks:
Question 1. (25 points)l
Use Laplace transforln to solve:
2'1) w 2y(t) + m = (2
gm) a we) a 1
] 1101'muias:
Ut'l] : 7;! EM! 2
Topic 1: Introduction to Statistics Exercises
Q1
For each of the following variables, determine whether the variable is categorical or
numerical. If the variable is numerical, determine whether the variable is discrete or
continuous.
Number of cell phones
Topic 3: Discrete and Continuous Probability Distributions Exercises
Q1
In a recent survey concerning the age (to the nearest year) and weight (to the nearest 10 lb) of
first-year university students, the following probability distribution was obtained:
A
Topic 4: Sampling Distributions Exercises
Q1
Given a normal distribution with = 100 and = 12, if you select a sample of n = 36, what
is the probability that
is
X
a)
b)
c)
d)
Less than 95?
Between 95 and 97.5?
Above 102.2?
There is a 65% chance that
is abo
Topic 1: Introduction to Statistics Solutions
Q7
a) Population Mean, = 6
b)
Population Variance,
2
= 10.2
Population Standard Deviation,
= 3.1937
Q8
Mean,
=
X
23.5 19.8 21.3 22.6 19.4 18.2 24.7 21.9 20.0 21.1
10
Standard Deviation, S =
=1.9896
2
(23.5 21.
Topic 3: Discrete and Continuous Probability Distributions Solutions
Q1
a)
1 0.02 0.09 0.09 0.01 0.02 0.06 0.15 0.05 0.03
0.02 0.06 0.11 0.04 0.05
0 . 2
b)
Probability distribution of weight
Weight
100
110
Probabilit 0.1
0.3
y
c)
Expected Weight =
d)
St
Topic 2: Basic Probability Solutions
Q1
Needs warrantyrelated repair
Yes
No
Total
U.S.
Non-U.S.
Total
0.025
0.575
0.600
0.015
0.385
0.400
0.04
0.96
1.00
a)
P(needs warranty repair) = 0.04
b)
P(needs warranty repair and manufacturer based in U.S.) = 0.025
Topic 5: Confidence Interval Estimation Exercises
Q1
If
=120, =24 and n=36, construct a 99% confidence interval estimate of the population
X
mean,
Q2
A stationery store wants to estimate the mean retail value of greeting cards that it has in its
inventory
Topic 1: Introduction to Statistics Solutions
Q1
a)
b)
c)
d)
Numerical, discrete
Numerical, continuous
Categorical
Categorical
Q2
a) and b)
Frequency
4
7
9
13
9
5
3
$80 - Less than $100
$100 Less than $120
$120 Less than $140
$140 Less than $160
$160 Less
Topic 2: Basic Probability Exercises
Q1
Each year, ratings are compiled concerning the performance of new cars during the first 90
days of use. Suppose that the cars have been categorized according to whether the car needs
warranty-related repair (yes or