UNIVERSITY OF BOTSWANA DEPARTMENT OF MATHEMATICS Question One MAT 271 TEST 1 Let a random variable W be given by WZ+Z+...+Zo where Z, are independent standard normal random variables for i = 1, 2, ..., 10. Find P(3.247W < 20.483) [7 marks] x-x Z = ก Question Two A boy flips a fair coin 100 independent times and a girl flips a fair coin 100 independent times. What is the probability that the boy will have 10 less tails than the girl? Question Three [7 marks] The random variable, X, representing the number of ice blocks in a drink, has the following probability distribution. H 4 5 6 7 f(x) = P(X = 1) 0.2 0.4 0.3 0.1 Find, using the normal approximation, the probability that in a sample of 36 drinks, the average number of ice blocks will be less than 5.5. [8 marks] P (W < 3.247) - P (W220.483) - 5.1 4-4-9 + -5 + - 5.2 253 1 p(x <5.5)=1 <)+(01)+5(04)+(0-3) + 7 (0.1) 1. (**)+(0,2)+5" (0.4)+6°² (0-3)+21 (0+1) 29.9 1=36 ०=०.११
UNIVERSITY OF BOTSWANA DEPARTMENT OF MATHEMATICS Question One MAT 271 TEST 1 Let a random variable W be given by WZ+Z+...+Zo where Z, are independent standard normal random variables for i = 1, 2, ..., 10. Find P(3.247W < 20.483) [7 marks] x-x Z = ก Question Two A boy flips a fair coin 100 independent times and a girl flips a fair coin 100 independent times. What is the probability that the boy will have 10 less tails than the girl? Question Three [7 marks] The random variable, X, representing the number of ice blocks in a drink, has the following probability distribution. H 4 5 6 7 f(x) = P(X = 1) 0.2 0.4 0.3 0.1 Find, using the normal approximation, the probability that in a sample of 36 drinks, the average number of ice blocks will be less than 5.5. [8 marks] P (W < 3.247) - P (W220.483) - 5.1 4-4-9 + -5 + - 5.2 253 1 p(x <5.5)=1 <)+(01)+5(04)+(0-3) + 7 (0.1) 1. (**)+(0,2)+5" (0.4)+6°² (0-3)+21 (0+1) 29.9 1=36 ०=०.११
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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Related questions
Question
![UNIVERSITY OF BOTSWANA
DEPARTMENT OF MATHEMATICS
Question One
MAT 271 TEST 1
Let a random variable W be given by WZ+Z+...+Zo where Z,
are independent standard normal random variables for i = 1, 2, ..., 10. Find
P(3.247W < 20.483)
[7 marks]
x-x
Z =
ก
Question Two
A boy flips a fair coin 100 independent times and a girl flips a fair coin 100
independent times. What is the probability that the boy will have 10 less
tails than the girl?
Question Three
[7 marks]
The random variable, X, representing the number of ice blocks in a drink,
has the following probability distribution.
H
4 5 6 7
f(x) = P(X = 1) 0.2 0.4 0.3 0.1
Find, using the normal approximation, the probability that in a sample of
36 drinks, the average number of ice blocks will be less than 5.5. [8 marks]
P (W < 3.247) - P (W220.483)
- 5.1 4-4-9 + -5 + - 5.2
253
1
p(x <5.5)=1
<)+(01)+5(04)+(0-3) + 7 (0.1) 1.
(**)+(0,2)+5" (0.4)+6°² (0-3)+21 (0+1)
29.9
1=36
०=०.११](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2006393e-c97e-4081-8173-0190425f3dd9%2Fd9cedec8-cb59-4550-95a1-027d0eb290d3%2Fhs3w6kj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:UNIVERSITY OF BOTSWANA
DEPARTMENT OF MATHEMATICS
Question One
MAT 271 TEST 1
Let a random variable W be given by WZ+Z+...+Zo where Z,
are independent standard normal random variables for i = 1, 2, ..., 10. Find
P(3.247W < 20.483)
[7 marks]
x-x
Z =
ก
Question Two
A boy flips a fair coin 100 independent times and a girl flips a fair coin 100
independent times. What is the probability that the boy will have 10 less
tails than the girl?
Question Three
[7 marks]
The random variable, X, representing the number of ice blocks in a drink,
has the following probability distribution.
H
4 5 6 7
f(x) = P(X = 1) 0.2 0.4 0.3 0.1
Find, using the normal approximation, the probability that in a sample of
36 drinks, the average number of ice blocks will be less than 5.5. [8 marks]
P (W < 3.247) - P (W220.483)
- 5.1 4-4-9 + -5 + - 5.2
253
1
p(x <5.5)=1
<)+(01)+5(04)+(0-3) + 7 (0.1) 1.
(**)+(0,2)+5" (0.4)+6°² (0-3)+21 (0+1)
29.9
1=36
०=०.११
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