THE INTERNATIONAL UNIVERSITY (IU) Course: Statistics for Business
Department of Business Administration MIDTERM EXAMINATION
STATISTICS FOR BUSINESS Duration: 120 minutes
Dean of School of Business Lecturers: Student ID: Date: November 7 th , 2015 Name: Dr. Nguyen Van Phuong Ass. Prof. Ho Thanh Phong Dr. Ha Thi Xuan Chi Dr. Phan Nguyen Ky Phuc Ho Thanh Vu INSTRUCTIONS: 1.
This is an opened book examination. 2. Calculator is allowed. 3.
Laptop, mobile phone, discussion and materials transfer are strictly prohibited. 4.
There are 2 parts in this exam. Total pages: 05 (including this page)
PART I: MULTIPLE CHOICE QUESTIONS (30%):
Please select the correct answer for the following questions. You must write your answers on the answer
sheet. Each correct answer scores 2 points. (30 points)
1. A new drug has been developed and tested. It works (effective) 65% of the time. A group of 7 patients have
tried the drug. What is the probability at least 3 person will be cured by the drug? A. 0.944 B. 0.923 C. 0.895 D. None of the above
1 – 0.357 – 0.356*0.65*C(7,6) – 0.355*0.652*C(7,5)
2. C2 Green tea bottle are promised to contain a certain amount of liquid inside. Given that the volume of
green tea inside are distributed with mean = 350ml and standard deviation = 70 ml. A student bought 40
bottles. What is the probability that volume of green tea from these bought bottles exceed 375 ml? A. 0.050 B. 0.024 C. 0.067 D. None of the above
3. Given data set: 0.76; 1.71; 0.34; 1.84; 1.06; 0.93; 2.13; 2.11 Calculate the upper and lower quartile
Statistics for Business – Midterm Exam
THE INTERNATIONAL UNIVERSITY (IU) Course: Statistics for Business
Department of Business Administration A. 0.803 – 2.043 B. 0.703 – 1.943 C. 0.903 – 2.143 D. None of the above
4. Given data set: 81; 15; 21; 72; 99; 12; 20; 85; 32; 98; 16. Calculate the mean of the data set A. 50.091 B. 63.106 C. 58.582 D. None of the above 5.
Given data set of a sample: 6.21; 28.5; 22.98; 19.82; 17.48. Calculate the variance A. 69.735 B. 57.183 C. 64.925 D. None of the above 6.
An IT company surveys on types of laptops their employees are using. Data is distributed as follow ASUS Dell Sony Male 42 3 15 Female 5 7 15 87 employees
Choosing an employee at random. What is the probability that it is a male employee using ASUS laptop? A. 0.500 B. 0.613 C. 0.413 D. None of the above 7.
What is the probability that the team has exactly 1 manager, 1 IT guy and 3 engineers A. 0.426 B. 0.357 C. 0.246 D. None of the above 8.
What is the probability that the team has 4 engineers A. 0.029 B. 0.032
Statistics for Business – Midterm Exam
THE INTERNATIONAL UNIVERSITY (IU) Course: Statistics for Business
Department of Business Administration C. 0.024 D. None of the above
These below data are used for question #9 and #10
Amount of money a gambler earns after playing a game of card is distributed in the table below: X P(X) -1 0.2 0 0.05 1 0.15 2 0.35 3 0.25 9.
What is the probability that the gambler earns money A. 0.7 B. 0.75 C. 0.8 D. None of the above 10.
What is the expected value of the gambler’s money A. 1.1 B. 1.2 C. 1.3 D. None of the above 1.4 11.
Battery life is known to be normally distributed with mean of 2 years and standard deviation of 0.5
year. Every day, at facility X, a number of 10000 batteries are produced. Find the number of batteries
have lifetime less than 23 months A. 0.511 B. 0.498 C. 0.566 D. None of the above 4338
Statistics for Business – Midterm Exam
THE INTERNATIONAL UNIVERSITY (IU) Course: Statistics for Business
Department of Business Administration 12.
Let X be a normal distribution with mean 120 and variance 25. Determine 2 value: a and b, symmetric
around the mean, such that they cover 95% of the data (confidence interval) A. 115.1 – 125.2 B. 110.2 – 129.8 C. 100.6 – 128.5 D. None of the above 13.
Exam grading in a Statistics class are known to follow normal distribution with mean 73 points and
standard deviation of 11 points. Given a class of 68 students, how many students score from 81-89
points in the exam? (round up to the nearest integer) A. 11 B. 13 C. 15 D. None of the above 14.
Let X be a binomial random variable with E[X] = 6.4, Var(X) = 1.28. Calculate P(X = 3) A. 0.0092 B. 0.0076 C. 0.0083 D. None of the above 15.
There are 2 boxes, 1 containing 1 black marble and 1 white marble. The other one has 2 black marbles
and 1 white marble. We select one box at random, then select randomly 1 marble in that box. What is
the probability that the 1st box was selected, given the selected marble was white A. 0.2 B. 0.3 C. 0.4 D. None of the above
PART II: WRITTEN QUESTIONS (70%) Question: 1. Question 1: 10 pts
Given a data set of a sample as follow:
12, 14, 13, 11, 27, 20, 11, 12, 29, and 12
Statistics for Business – Midterm Exam
THE INTERNATIONAL UNIVERSITY (IU) Course: Statistics for Business
Department of Business Administration
a. Find the upper quartile, 22nd, 97th, 68th percentile (4 pts)
b. Calculate the mean and variance of the data set (4 pts)
c. Another sample data set are given as follow:
18, 17, 3, 5, 1, 34, 39, 28, 6, and 10
What is your interpretation about 2 sample mean and variance and the behavior of 2 data sets? (2 pts) 2. Question 2: 15 pts
A marble is drawn randomly from an urn containing 6 white and 4 black marbles. After a marble is drawn,
it is replaced and another marble is drawn again. This process goes on indefinitely.)
a. What is the probability that, of the first 4 marbles drawn, exactly 3 are white (5 pts)
(63 x 4 x C(4,3)) / 104 = 0.3456
b. What is the probability that, of the first 6 marbles drawn, there are at least 3 white (5 pts)
1 – (46 + 45x6xC(6,5) + 44x62xC(6,4))/106 = 0.8208
c. 5 red marbles are added into the urn. What is the probability that, of the first 9 marbles drawn, exactly 5 are red (5 pts)
No replacement: (5*4*3*2*1*104*C(5,9)) / (15*14*13*12*11*104) =0.042
Replacement: (55*104*C(9,5)) / 159 = 0.102 3. Question 3: 15 pts
Scientists in Weather Forecasting Department have been working really hard and finally came to the
conclusion that the annually rainfall of Xuân Lộc-Đồng Nai is normally distributed with mean 1.956mm,
and standard deviation of 0.215 mm.
a. What is the probability this year’s rainfall will over 2.2mm? (5 pts) 0.128
b. What is the probability that the sum of the next 2 years’ rainfall will less than 4mm? (5 pts) 0.58
c. What is the probability that the sum of the next 3 years’ rainfall will exceed 5.89mm? (5 pts) 0.47661 4. Question 4: 15 pts
A life cycle of a ladybug includes three stages, namely, egg, larva, pupa and adult. The probability that an
egg can survive and become a larva is 0.7. The probability that a larva can survive and become a pupa is
0.6. The probability that a pupa can survive and become an adult is 0.5. Assume that there are 100 eggs.
a. Find the probability a randomly selected egg has survived to pupa stage (5 pts) 0.7*0.6=0.42
b. Find the expected number of adults. (5 pts) 0.7*0.6*0.5*100=21
Statistics for Business – Midterm Exam
THE INTERNATIONAL UNIVERSITY (IU) Course: Statistics for Business
Department of Business Administration
c. If we know that an egg cannot become an adult, what is the probability that it died at larva stage, pupa stage? (5 pts)
Cannot become an adult: 1-0.7*0.6*0.5=0.79
Larva stage: (0.7*0.4)/0.79=0.35
Pupa stage: (0.7*0.4*0.5)/0.79=0.27 5. Question 5: 15 pts
The probability of variable X is given as follow Demand Probability ( X ) 1 0.1 2 0.2 3 0.4 4 0.2 5 0.1
a. Find the cumulative probability distribution for X, then calculate the expected value of X (5 pts) f x( ) 2 b. x- 3x
Find the expected value and variance of the function 2 . (6 pts)
c. Given X is a demand of a product. The purchasing cost of one unit of this product is 4. The unit selling
price is 6. If we purchase more than demand we will lost -1 for each unit cannot be sold. Find the optimal
purchasing quantity. (4 pts)
PLEASE SHOW YOUR WORK IN THE WRITTEN QUESTIONS PART GOOD LUCK!
Statistics for Business – Midterm Exam