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‫أستاذ المادة‬
: ‫رقم الشعبة أو وقتها‬
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: ‫اسم الطالب‬
: ‫رقم الطالب‬
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Final Exam – QM 120 – Spring 2001/2002
Question (1)
For the following 12 questions choose only 10 of them and answer them by ticking the right answer:
1- Conditional probability of an event is always:
(a) Smaller than the unconditional probability of the same event.
(b) Larger than the unconditional probability of the same event.
(c) Could be larger or smaller than the unconditional probability of the same event.
2- A 95% confidence intervals for the population mean (  ) means that if we take 100 samples with
the same sample size and construct 100 such confidence intervals for  , then:
(a) 95 of them will not include 
(c) 95 of them will include 
(b) 95 of them will include the sample average X
(d) none of the above
3- The parameters of the normal distributions are
(a)  , Z, and 
(b)  and 
(c) , X, and 
(d) n and P
4- If X is a random variable that follows the normal distribution with mean  and standard deviation
 . The standardized (Z) value for any value of X that is less than the mean () is always:
(a) positive
(b) negative
(c) 0
5- The number of combinations of 10 items selected 7 at a time (i.e. 10 combinations 7) equal:
(a) 120
(b) 200
(c) 80
(d) none of the previous
(c) p, and q
(d) n, p, and x
6- The parameters of the binomial distribution are:
(a) n, p, and x
(b) n, p, and q
7- The collection of all outcomes for an experiment is called:
(a) An event
(c) Distribution function
(b) the probability mass function
(d) a sample space
8- If the random variable X has a binomial distribution with mean 2 and variance 1.8, then the
probability that the random variable X takes a value that is less than or equal to 3 is:
(a) 0.2852
(b) 0.1901
(c) 0.8099
(d) none of the previous
9- Which of the following is the mean of the squared deviations of X from its mean?
(a) variance
(b) range
(c) mean
(d) standard deviation
10-The percentage of data lying inside the box of the box and whiskers plot is:
(a) 25% of the data
(b) 50% of the data
(c) 75% of the data
(d) we do not know
11- For the standard normal random variable Z, the probability that Z equal to 0 is:
(a) 0.5
(b) - 0.5
122 mutually exclusive events are:
(a) Independent events
(b) dependent events
(c) 0
(d) we do not know
(c) neither a, nor b
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Question 2-Part I
Suppose that airplanes arrive to a certain airport according to a Poisson distribution with mean rate
of 8 airplanes per hour. Find the following:
(a) Write down the probability density (mass) function of the above distribution.
(b) What is the probability that exactly 5 aircrafts arrive during a (1-hour) period? At least 2? At
most 2?
(c) What is the expected value of the number of airplanes that arrive during (90 – minutes period) and
what is its standard deviation?
Part II
If for all repair work done on TV sets by a certain store, 80% is done on sets that are no longer under
warrantee and 20% are done on TV sets that are still under warrantee. Among the next 10 sets
brought in for repair find out the following:
(a) Write down the probability density function for the number of sets that is no longer under
warranty, among those brought in for repair.
(b)What is the expected value of the number of sets that are not under warranty? Its variance and its
standard deviation?
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(c) Among these 10 sets, what is the probability that exactly 75% sets are not under warranty?
(d) What is the probability that between 5 and 8 inclusive (5 and 8 are included) are not under
warranty?
(e) What is the probability that at least 9 sets are under warranty?
Question 3-(Part I)
The following are the number of credit cards issued per day at a local bank for the last 25 days:
10, 12, 11, 19, 22, 21, 23, 22, 24, 25, 23, 21, 28, 26, 27, 27, 29, 26, 22, 28, 30, 32, 25, 37, 34
Compute the following:
(a) The average number of credit cards issued by the bank per day
= _____________
(b) The standard deviation of the credit cards issued by the bank per day= ____________
(c) The median number of credit cards issued by the bank per day = ____________
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(d) The mode number of credit cards issued by the bank per day =_________________
Part II
A university president has proposed that all students must take a course in ethics as requirement for
graduation. Four hundred faculty members and students from this university were asked about their
opinion on this issue. The following table gives two-way classifications of the responses of theses
faculty members and students
Respondents
Favor ( B 1 )
Oppose ( B 2 )
Neutral ( B 3 )
Faculty ( A 1 )
50
30
20
Student ( A 2 )
120
130
50
Total
170
160
70
Total
100
300
400
(a) If an individual is selected at random, what is the sample space of this random experiment?
(b) What is the probability that a selected individual is a faculty member and apposed the issue?
(c) What is the probability that the selected individual is not a faculty member or does not appose the
issue?
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(d) Complete the probability tree where events ( A 1
or A 2 ) occur first and events
( B 1 or B 2 or B 3 ) occur next.
(e) What is the probability that a certain individual is in favor of the issue?
(f) If an individual had been selected at random and was asked about his opinion regarding the issue
and he/she answered that he/she is not in favor of that issue. What is the probability that he/she is
a faculty member?
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Question 4
Suppose that an instructor gives an accounting exam where scores followed the normal distribution
with an average (mean) score of 85, and standard deviation of 10. Use the normal distribution to
answer the following for a sample of 50 students selected at random from that class:
(a) What is the distribution of the mean (average) score of the 50 students? Its mean and its
standard deviation?
(b) What is the probability that the average (the mean) of the 50 students is at least 80?
(c) What is the probability that the average (the mean) scores of the 50 students is at most 90?
(d) What is the probability that the average (the mean) of the 50 students lies between 83 and 88?
Question 5:
The management at a large insurance company believes that workers are more productive if they are
happy with their jobs. To keep track of workers satisfaction, the company regularly conducts surveys.
According to a recent survey, the mean job satisfaction score for all workers at this company was 13.1
(on a scale of 1 to 20) and the standard deviation was 1.95 . Assume that job satisfaction scores of
workers are normally distributed. Answer the following:
(a) Find the probability that the job satisfaction score of a randomly selected worker from this
company is less than 11.50
(b) What percentage of workers has a job satisfaction scores between 14.5 and 18.5?
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(c) A worker with score of 8 or less is considered to be unhappy with the job. What percentage of
the workers is unhappy with their jobs?
(d) What is the satisfaction score that the management considers for the top 5% very happy
workers with their jobs?
Question 6:
A hotel owner has determined that 80% of the hotel’s guests eat either breakfast or dinner in the hotel
restaurant. Further investigation reveals that 30% of the guests eat dinner (event A) and 60% of the
guests eat breakfast (event B) in the hotel restaurant. Draw Venn diagram, hence answer the
following questions
(a) If a guest is selected at random and asked where he usually have his breakfast and dinner. What
is the sample space of this experiment?
(b) What proportion of the hotel guests eat both dinner and breakfast in the hotel restaurant?
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(c) What proportion of hotel guests does not eat dinner or does not eat breakfast in the hotel
restaurant?
(d) What proportion of hotel guests eat dinner but not breakfast in the hotel restaurant?
(e) What proportion of hotel guests who eat only one meal of the two meals?
(f) If we know that a hotel guest ate his/her dinner in the hotel restaurant, what is the probability
that he did not eat his breakfast in the hotel restaurant?
(g) Are events A and B mutually exclusive? Justify?
(h) Are events A and B independent? Justify?
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