Graduate School of Business – MBA program

Final Exam
Course: Applied Statistics Marks: 60
Lecturer: Prof. Nasser El-Maghraby Duration: 2 Hours

Answer Four Questions Only

1.a) Find the correlation coefficient and the regression equation of the form (y= ax +b) for
the following data
x 3 5 7 9 11 13 15
y 16 14 12 10 10 8 6
b) Evaluate the rank correlation coefficient for the following table

Math. F F A B+ F C D C D
Stat. F D C F B A B C+ A

2.a) The department of languages & humanities in a college found that 25% of students
withdraw the statistics course without completing it. Assume that 20 learners have
registered for the course in the summer semester. What is the probability that:
i) 17 will complete the course?
ii) At least three will withdraw the course?

b) If 2% of new portable computers are defective. Assume that we will randomly select
210 portable computers and that we are interested in the number of defective computers.
Compute the following probabilities:
i. Finding exactly four defective.
ii. Finding two or fewer defective.

3. a) Three students in a swimming race if the probability of the first is double the
probability of the second and the probability of the third equal six times the probability of
the second. Find the probability that the first or the second wins.

b) Three dice are tossed Find :

i) The probability of getting three numbers whose sum less than 5
ii) The probability of getting three numbers whose sum less than or equal 17

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4. a) A recent survey found that 37% of the Mexican teenagers are alcoholic. A random
sample of 20 Mexican teenagers revealed that 15 of them are not alcoholic. Can we
conclude that the percentage of the alcoholic have bean changed? use α = 0.01

b) The time needed to complete final examination in a particular college course is

normally distributed with a mean of x minutes and standard deviation  minutes

i) Find the value of the mean if the value of the standard deviation is 10 and the
probability of completing the exam in more than 72.4 minutes is 0. 1038.
ii) Find the value of the standard deviation if the value of the mean is 70 and the
percentage of the students whom complete the exam in more than 61.2 minutes is
86.43% ?

5. a) A survey provided the estimate that the mean number of hours of using internet per
household is 6.4 hours per day. Assume that the survey involved 115 households and the
sample standard deviation was 1.9 hours per day. Five years ago, the population mean
number of hours of internet using per household was reported to be 4.6. Can we conclude
that the mean number of hours of using internet per household have bean changed?
use α = 0.05

b) The suppliers provide the following data on defective parts .

Supplier A B C
Good 85 70 55
Minor Defect 80 56 44
Major Defect 105 174 101

Use  = 0.1 , test for independence between Supplier and part quality .

Good Luck

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 Rules
Pearson’s correlation coefficient
Regression
n∑ xy - (∑ x)(∑ y )
n∑ xy - (∑ x)(∑ y ) r=
2 2
a= 2 n∑ x 2 - (∑ x ) n∑ y 2 - (∑ y )
n∑ x 2 - (∑ x)
Rank correlation coefficient
∑ y - a∑ x 6  D2
b= r  1
n
n ( n 2  1)
n(A )
P (A ) 
n (s ) P(A)  1  P(A)
P A  B   P A   P B   P  A  B 

n x n!
P  x   nC x  x 1    Cx 
n

x !n  x  !

e   x   n
P x  
x!
  x 
E z E t z 
n n 

p 1  p  p 1  p 
E z E t df  n  1
n n

  f  f 2   Row total Column total

c2    o e
 fe 
 fe  Grand total

d.f. = (number of rows -1)(number of columns -1)

Confidence level Z
90% 1.65
95% 1.96
99% 2.58

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