BUS 102 Arab Open University Introduction to Statistics Exam Please answer the questions correctly. The questions and formulas are all in the uploaded file

BUS 102 Arab Open University Introduction to Statistics Exam Please answer the questions correctly. The questions and formulas are all in the uploaded file. Faculty of Business Studies
BUS102
Introduction to Statistics
Final Examination – THE – Version A
2019-2020 /Summer Semester
Number of Exam Pages: 10
(including this cover sheet(
Time Allowed: 48 hours
Grades
Question
Number
Question 1
Question 2
Question 3
Question 4
Question 5
Total in Figures
Total in Letters
Total grade allocated
for this question
20
20
20
20
20
100
Student’s
earned grade
Marker Name and Signature
Instructions
1. This examination consists of Five questions. You are required to answer all questions.
2. Keep in mind that any form of cheating will not be tolerated and will subject you to AOU
cheating policy.
3. Show all calculations in your answers
BUS102/ THE-Final – Ver A
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Take Home Exam for Final Assignment 2019-2020/Second
BUS102 – An Introduction to Statistics
Cut-Off Date : 21st July 2020
Cut off Time: 4:05 PM
Total Marks
Duration: 48 Hours
: 100
Contents:
Warnings and Declaration……………………………………….………………………………………………………………. 2
Question1 ……….…………………………………………………………………………………………….…………………….…. 3
Question 2 ……………………………………………………………………………………………………………….………………4
Question3 …………………………………………………………………………………………………………………………………5
Question 4 ………….…………………………………………………………………………………………………………….……….6
Question 5………………………………………………………………………………………………………………………………….7
Table Values……………………………………………………………………………………………………………………………8 – 13
Plagiarism Warning:
As per AOU rules and regulations, all students are required to submit their own THE-Final work and avoid plagiarism.
The AOU has implemented sophisticated techniques for plagiarism detection. You will be penalized for any act of
plagiarism as per the AOU’s rules and regulations.
Declaration of No Plagiarism by Student (to be signed and submitted by student with THE-Final work):
I hereby declare that this submitted THE-Final work is a result of my own efforts and I have not plagiarized
any other person’s work.
Name of Student: ————————————————————————Student ID No.—————————————————————————Signature: …………………………..…………………………………………………………………..
Section No. ———————————————————————————–Date:………………………………………………………………………………………………….…………
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Question 1: (20 points)
(A) The number of laptops sold daily at a local electronics shop has the following probability
distribution.
X: No. of laptops sold
P(X=x)
12
0.4
13
0.3
14
0.2
15
0.1
a) What is the mean of the number of laptops sold on a given day?
= ∑ .P(X) = 12*0.4 + 13*0.3 + 14*0.2 + 15*0.1 = 13
b) What is the variance of the number of laptops sold on a given day?
2 =∑ 2 .P(X) – 2
2 = 122 *0.4 + 132 *0.3 + 142 *0.2 + 152 *0.1 – 132
2 = 170-132 = 170-169 = 1
(B) A new drug claims to be effective against flu 70% of the time. The drug is tested on 28
selected patients.
a) Use Binomial distribution to find the probability that exactly 21 patients recovered from
the flu? (Round your answer to the nearest thousandth).
b) What is the mean of the number of patients who recovered from the flu?
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c) What is the variance of the number of patients who recovered from the flu?
(10 + 10 = 20 marks)
Question 2 (20 points)
A class consists of 12 boys and 10 girls. A committee of 5 students is to be selected to represent
their class in a musical competition:
a) What is the probability of having exactly 1 girl in the committee? (Round your answer to
the nearest thousandth).
b) What is the probability of having exactly 3 boys in the committee? (Round your answer
to the nearest thousandth).
(12 .5 + 7.5 = 20 marks)
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Question 3: (20 points)
(A) The amount of tea leaves in a can from a particular production line is normally distributed
with μ (mean) = 110 grams and σ (Standard deviation) = 5 grams.
(i) What is the probability that a randomly selected can will contain less than 105 grams of tea
leaves?
−
105−110
Z= =
= -1
5
P(105 grams < weight < 110 grams ) 0.3413 P(weight < 105 grams ) = 0.5 – 0.3413 = 0.1587 (ii) If a sample of 9 cans is selected, what is the probability that the sample mean of the content “tea leaves” to be more than 115 grams? − Z = / √ = 115−110 5/√9 =3 P (110 grams < weight < 115 grams ) = 0.4987 P ( weight > 115 grams ) = 0.5 – 0.4987 = 0.0013
(B) In a city, it is estimated that the maximum temperature in July is normally distributed with a
mean of 23º and a standard deviation of 4°. Calculate the probability of having a maximum
temperature between 20° and 28°
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(6 + 6 + 8 = 20 marks)
Question 4: (20 points)
(A) The weight of cans of vegetables is normally distributed with a mean of 1000 grams and a
standard deviation of 50 grams. What is the probability that the sample mean of weight for 10
randomly selected cans is more than 1040?
(B) The age of vehicles registered in a certain European country is normally distributed with a
mean of 98 months and a standard deviation of 15 months. What is the probability that the
sample mean of age for a sample of 36 vehicles is between 100 and 102 months?
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(10 + 10 = 20 marks)
Question 5: (20 points)
(A) A major store is interested in estimating the mean amount its credit card customers spent on
their first visit to the chain’s new store. Fifteen credit card accounts (n=15) were randomly
sampled and analyzed with the following results: X = $50.50 and S = 20.
a) Construct a 95% confidence interval for the mean amount its credit card customers spent on
their first visit to the chain’s new store.
b) Interpret the results (the interval) you got.
(B) A quality control engineer is interested in estimating the proportion of defective items
coming off a production line. In a sample of 200 items, 28 are defective.
a) Find the 95% confidence interval for the proportion of defectives from this production
line
b) Interpret the results (the interval) you got.
(10 + 10 = 20 marks)
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End of Questions
KEY FORMULAS
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Areas under the standard normal curve
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Student’s t distribution
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