THE UNIVERSITY OF HONG KONG
DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE
STAT 0301 Elementary Statistical Methods
Assignment 3
(No need to hand in. Do all in preparation for the class test 9/3/2011.)
*1.
Alan participates in an athletics competition.
The game consists of 5 items.
Alan’s
performance in each item follows a normal distribution with mean and s.d.
(both in
points) as follows:
Item (
i
)
1
2
3
4
5
Mean (
μ
i
)
85
90
80
93
78
S.D. (
σ
i
)
4
3
5
2
6
If Alan’s performances are independent from game to game, what is the probability that
(i) his total score equals 450 points?
(ii) his total score exceeds 450 points?
(ii) his average score exceeds 60 points?
2.
An examination consists of 4 papers. Betty’s performance in each paper has a normal
distribution with mean and s.d. (both in marks) as follows:
Paper (
i
)
1
2
3
4
Mean (
μ
i
)
70
58
75
55
S.D. (
σ
i
)
3
7
4
5
If Betty’s performances are independent from paper to paper, what is the probability
that
(i) her total marks will exceed 280?
(ii) her average marks will exceed 60?
3.
David’s monthly income and expenditure are both normally distributed. They perform
independently, with means and s.d.’s as follows:
Parameter
Income
Expenditure
Mean (
μ
i
)
$8500
$7300
S.D. (
σ
i
)
$550
$850
(a) What is the probability the he will be in red next month?
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '11
 Gabrille
 Statistics, Normal Distribution, Standard Deviation, Probability theory, S.D.

Click to edit the document details