University of Prince Edward Island/ Universities of Canada
BUS2510 / FALL 2022
Name: …………………..
UofCanada ID: ……………………
Assignment 7
UofCanada Egypt
Module Title: BUS 2510: Intro to Managerial Science
Module Leader: Dr. Yasmine M. Abdeldfattah
Fall 2022
Student name:
ID:
Instructions to Students
•
•
•
Justify all your work.
For questions which require a written answer, show all your work and the used formula.
Full credit will be given only if the necessary work is shown justifying your answer.
Problem 1:
The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and
a standard deviation of 15. You enrolled in a class of 25 students. What is the probability
that the class’s IQ exceeds 130?
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University of Prince Edward Island/ Universities of Canada
BUS2510 / FALL 2022
Problem 2:
A marine biologist would like to identify the least polluted coastal areas in the United
States. A study shows that there is an average increase is 30% in fertilizer and nitrogen
discharge with standard deviation of 13%. The observations follow a normal distribution.
What is the value that would correspond to the least 20% polluted coastal areas from this
study?
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University of Prince Edward Island/ Universities of Canada
BUS2510 / FALL 2022
Problem 3:
The weekly mean income of a group of executives is $1000 and the standard deviation
of this group is $100. The distribution is normal. What percent of the executives have
an income of $1100 or more?
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University of Prince Edward Island/ Universities of Canada
BUS2510 / FALL 2022
Problem 4:
An analysis of the grades on the final exam in Finance 101 is revealed that they
approximate a normal curve with a mean of 75 and a standard deviation of 8. The
instructor wants to select the worst 7 % of the class. What is the dividing grade of this
group?
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University of Prince Edward Island/ Universities of Canada
BUS2510 / FALL 2022
Problem 5:
The owner of Britten’s Egg Farm wants to estimate the mean number of eggs produced
per chicken. A sample of 20 chickens shows they produced an average of 20 eggs per
month with a standard deviation of 2 eggs per month.
a) What is the value of the population mean? What is the best estimate of this
value?
b) Explain why we need to use the t distribution. What assumption do you need to
make?
c) For a 95% confidence interval, what is the value of t?
d) What is the margin of error?
e) Develop the 95% confidence interval for the population mean.
f) Would it be reasonable to conclude that the population mean is 21 eggs? What
about 25 eggs?
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University of Prince Edward Island/ Universities of Canada
BUS2510 / FALL 2022
Problem 6:
The average cost of tuition, room and board at small private liberal arts colleges is
reported to be $8,500 per term, but a financial administrator believes that the average
cost is higher. A study conducted using 350 small liberal arts colleges showed that the
average cost per term is $8,745 with a standard deviation of $1,200. At 0.03 significance
level, test the financial administrator’s claim.
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University of Prince Edward Island/ Universities of Canada
BUS2510 / FALL 2022
Problem 7:
A Washington, D.C., “think tank” announces the typical teenager sent 67 text messages
per day in 2017. To update that estimate, you phone a sample of 12 teenagers and ask
them how many text messages they sent the previous day. Their responses and their
summary statistics are as follows:
51, 175, 47, 49, 44, 54, 145, 203, 21, 59, 42, 100
Summary Statistics
Mean
82.5
Standard Error
17.17402
Median
52.5
Mode
#N/A
Standard
Deviation
59.49255
Sample Variance 3539.364
Kurtosis
0.034517
Skewness
1.183731
Range
182
Minimum
21
Maximum
203
Sum
990
Count
12
At the .01 level, can you conclude that the mean number is greater than 67?
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University of Prince Edward Island/ Universities of Canada
BUS2510 / FALL 2022
Problem 8:
The results of a statistics placement exam at UPEI for two campuses are as
follows:
Campus
Number
Mean
1
2
45
30
30
20
Pop Std.
Deviation
8
7
a. What is the null hypothesis if we want to test the hypothesis that the mean score
on Campus 1 is higher than Campus 2?
b. What is the computed value of the test statistic?
c. So, at a significance level of 𝛼 = 0.03, we would (circle one):
accept the null hypothesis / reject the null hypothesis / fail to reject the
null hypothesis
and conclude that [give your conclusion in the context of the problem of
interest and be as specific as possible about the direction and magnitude
of any effect] …………………………………
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University of Prince Edward Island/ Universities of Canada
BUS2510 / FALL 2022
Formula Sheet
𝜇=
𝛴𝑥
𝑁
𝑥̅ =
𝜎2 =
∑(𝑥 − 𝜇)2
𝑁
𝑃(~𝐴) =1−𝑃(𝐴)
𝑠2 =
∑(𝑥 − 𝑥̅ )2
𝑛−1
𝑃(𝐴 𝑜𝑟 𝐵)=𝑃(𝐴)+𝑃(𝐵)−𝑃(𝐴 𝑎𝑛𝑑 𝐵)
𝑃(𝑥) = 𝑛𝐶𝑥 𝑝 𝑥 (1 − 𝑝)𝑛−𝑥
𝑃(𝐴 𝑎𝑛𝑑 𝐵)=𝑃(𝐴)𝑃(𝐵│𝐴)
𝜇 = 𝑛𝑝
2
𝜎 = 𝑛𝑝(1 − 𝑝)
z=
𝑧=
𝑥−𝜇
𝜎
𝑧=
𝑥̅ − 𝜇
𝜎
√𝑛
𝑥̅ ± 𝑧
x̅1 −x̅2 −(μ1 −μ2 )
2
∑𝑥
𝑛
𝜎
√𝑛
2
σ
σ
√ 1+ 2
𝑧𝜎 2
𝑛=( )
𝐸
n1 n2
y ′ = a + bx
𝑏=
a=
∑y
∑x
−b
n
n
t=
𝑛(∑ 𝑥𝑦) − (∑ 𝑥)(∑ 𝑦)
𝑛(∑ 𝑥 2 ) − (∑ 𝑥)2
𝑟=
r√n − 2
√1 − r 2
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∑(𝑥 − 𝑥̅ )(𝑦 − 𝑦̅)
(𝑛 − 1)𝑠𝑥 𝑠𝑦