THE INTERNATIONAL UNIVERSITY (IU) Course: Statistics for Business School of Business INSTRUCTIONS:
1. This is an open book examination. Laptops, mobile phones are not allowed.
2. Use of calculator is allowed;
3. Discussion and material transfer are strictly prohibited.
Total pages: 04 (including this page)
PART I: Multiple-choice questions (30 points):
A teacher recorded the following exam scores (out of a possible 100 points) for 12 students. 45
50 53 55 77 87 90 92 95 96 99 100
1. Find the mean of the above sample: a) 88.45 b) 80.17 c) 90.61
d) None of the above, specify_________ Commented [M1]: 78.25
2. The 77th percentile of this sample is: a) 86.64 b) 85.47 c) Commented [M2]: 96.03
d) None of the above, specify__________
3. The probability of obtaining a value greater than 110 in a normal distribution in which the mean is 100 and the standard deviation is 10 is
______ the probability of obtaining a value greater than 650 in a normal distribution with a mean of 500 and a standard deviation of 100. a) less than b) Commented [M3]: greater than c) equal to
d) insufficient information to answer
4. In the standardized normal distribution, the probability that Z < 0 is: a) 0 b) 0.25 c) Commented [M4]: 0.5
d) None of the above, specify______________
Use the following data for the next 2 questions:
The lifetime of a battery is normally distributed with a mean life of 60 hours and a standard deviation of 3.4 hours. 1
Mid-term Exam – Statistics for Business
THE INTERNATIONAL UNIVERSITY (IU) Course: Statistics for Business School of Business
5. What is the probability that a randomly selected battery will last less than 57 hours? a) 0.6702 b) 0.5451 c) 0.3106 d) None of the above, specify__________
Commented [M5]: 0.1894
6. What is the probability that a randomly selected battery will last from 58 hours to 65 hours? a) 0.06516 b) Commented [M6]: 0.6516 c) 0.2068
d) None of the above, specify__________
7. Find the value of z if P(0 < Z < z) = 45% : a) 2.17 b) 2.575 c) 2.35 d) None of the above, specify__________ Commented [M7]: 1.645
8. There are 50 identical stamps with 16 stamps containing pictures and the remaining stamps
contain numbers. If the stamps were placed in a paper bag and thoroughly mixed, and you
select one of the stamps, do not replace it and select another. What is the probability that you
will randomly select a stamp with picture on the first draw and a stamp with number on the second draw? a) 1/2450 b) 136/625 c) 1/2
d) None of the above, specify____________ Commented [M8]: P(X) = 16/50*34/49 = 272/1225 = 0.222
Consider 4 boxes. Box A contains 7 red and 5 blue balls; box B contains 4 red and 6 blue balls,
box C contains 8 red and 8 blue balls and box D contains 6 red and 10 blue balls. A box is selected
randomly and a ball is randomly picked from the box.
9. What is the probability that it is a red ball? a) 1/8 b) 91/180 c) 5/12 d)
Commented [M9]: P(red) = 1/4(7/12 + 4/10 + 8/16 + 6/16) 223/480 2
Mid-term Exam – Statistics for Business
THE INTERNATIONAL UNIVERSITY (IU) Course: Statistics for Business School of Business
10. If P(A) = 0.4, P(B) = 0.65, and P(A | B) = 0.24, then P(A B) is: a) 0.0306 b) 0.124
d) None of the above, specify__________________
Commented [M10]: 0.894
11. Jack tosses a coin 3 times. What is the probability that he gets at most 2 Heads?
Commented [M11]: P(X) = 7/8 c) 0.306 a) 0.125 b) 0.875 c) 0.5
d) None of the above, specify__________
Use the following data for the next 2 questions:
The table below shows the numbers of boys and girls who are playing different kinds of sports in a sport club: Sport Football Basketball Badminton Boys 22 84 89 Girls 85 77 48 12. What is the probability that a randomly selected child in the club is playing football? a)
Commented [M12]: P(X) = (22+85)/405 0.264 b) 0.361 c) 0.425
d) None of the above, specify__________
13. What is the probability that a randomly selected child in the club is playing badminton given that the child is a girl? a) 0.379 b) 0.076 c) 0.119
d) None of the above, specify___________
Commented [M13]: P(X)=48/210
Use the following data for the next 2 questions:
A committee of 7 people to be selected randomly from a group of 10 men and 14 women. 3
Mid-term Exam – Statistics for Business
THE INTERNATIONAL UNIVERSITY (IU) Course: Statistics for Business School of Business
14. How many ways of selecting a committee with 3 men and 4 women? a)
Commented [M14]: 10 C3*14C4 120120 b) 4175 c) 0.347
d) None of the above, specify_____________
15. What is the probability that the committee will consist of more than 1 men? a) 0.4825 b) 0.2797 c) 0.8161 d) None of the above,
Commented [M15]: P(X>1) = 1 – P(X ≤ 1 ) = 0.903 (Using specify____________
hypergeometric with N = 24, S = 10, n = 7)
PART II: Writing (70 points): Question 1: (20 points)
A student recorded the weights (in grams) of a fruit that she achieved. The recordings were as follows:
874 887 991 1021 1034 1500 1679 2001 2014 Construct
the box plot for the above sample.
Question 2: (10 points)
The number of defects in a machine-made product is a random variable X with the following distribution: Number of defects x Probability P(x) 0 0.19 1 0.38 2 0.12 3 0.31
a) Find the mean and the standard deviation of the number of defects in a product?
b) Find the probability P(2 < X ≤ 4)? Question 3: (5 points)
A multiple-choice examination has 12 unrelated questions. Each question has five possible
answers, of which only one is correct. The probability that by just guessing, a student will get at most 8 correct is? 4
Mid-term Exam – Statistics for Business
THE INTERNATIONAL UNIVERSITY (IU) Course: Statistics for Business School of Business
Question 4: (15 points)
a) In an International Conference, there are 12 participants from different countries which
are assigned a seat next to each other on the same array. How many ways are there if
people A & B want to seat next to each other and C & D do not wish to seat next to each other?
b) James wishes to sell 2 books from his book collection: 5 Statistics books, 12 Physics
books & 3 Economics books. How many possible ways there are if those 2 books are different subjects?
Question 5: (20 points)
There is a game: player has to find out the way to exit a house at night. There is a light which is
turning on/off randomly: if the light is turned on, player has 28% chance knowing the way out; if the
light is turned off, player has probability of 0.2 to find out the way successfully. Assume the
probability that the light turned on is about 0.4.
a) What is the probability that the player will get the way out successfully?
b) What is the probability that the light was turned on given that player went out successfully? 5
Mid-term Exam – Statistics for Business