THE INTERNATIONAL UNIVERSITY (IU) Course: Statistics for Business
Department of Industrial System Engineering
MIDTERM EXAMINATION
STATISTICS FOR BUSINESS Duration: 120 minutes Head of School of Lecturer: Student ID: Date: Management 6 Apr, 2019 Name: Dr. Ho Nhut Quang Dr. Phan Nguyen Ky Phuc INSTRUCTIONS:
1. This is an open book examination. No laptops, PDA.
2. Use of calculator is allowed; discussion and material transfer are strictly prohibited. Total
pages: 2 (including this page)
PART II: SHORT QUESTIONS (100 %) Question 1: (15 pts)
The monthly revenues of a company in 2016 and 2017 is given in the table below (in million dollars) 78 90 60 121 112 89 110 100 95 114 65 80
a) Calculate mean, variance and standard deviation of this dataset
b) Calculate the values corresponding to 25th, 50th and 75th percentiles
c) Given values 93 and 105 find theirs corresponding percentiles. Question 2: (15 pts)
A person enrolls to a game. In each round, the player will toss a coin then record the face up value (Head
or Tail). The game ends after 3 Heads has appeared.
a) If the coin is the fair coin P(Head)=P(Tail)=0.5. Find the probability that the game ends exactly after 4 rounds
b) Now assume that there are 2 coins the first coin is fair, i.e. P(Head)=P(Tail)=0.5, the second coin is
unfair P(Head)= 0.7. Assume that at the beginning, one of coin is randomly selected, find the
probability that the game ends exactly after 4 rounds Question 3: (20pts)
Given the possible values and the corresponding probabilities of a discrete variable X X 0 100 200 300 400 P(X) 0.1 0.3 0.2 0.2 0.1
Statistics for Business- Midterm Exam 6,Apr, 2019 1
THE INTERNATIONAL UNIVERSITY (IU) Course: Statistics for Business
Department of Industrial System Engineering
It is known that X is a demand in a month of the market.
a) Find the expectation, variance and standard deviation of X
b) If for each scenario, the benefit is given by function Ā=3ÿ−2√ÿ. Find the expectation,
variance and standard deviation of Ā
c) The manager decides to manufacturing 350 items. If one item is sold, he obtains benefit of $4. For
one unsold item, he suffered the loss $-1.5. Find expectation, variance and standard deviation of
money that the manager can achieve. Question 4: (20pts)
A company intends to invest to a project which mainly consists of 3 costs, namely A, B and C. Given each
cost follows normal distribution as N (1000,300 ), N (2000,400 ) and N (3000,300 )
a) Find the probability that cost for A 2 2 A ≥8000≥12002 B E 2 C
b) Find the probability that total cost
c) If the budget for the payment of the company is N (3200,400 ) and the company has to pay only
half of the total cost. Find the probability that the company cannot afford this payment. Question 5: (20pts)
There are 2 boxes, A and B. Box A contains 5 red and 5 blue marbles. Box B contains 4 red and 6 blue
marbles. One box is selected randomly then two marbles are withdrawn in the 1st round. If they are the
same color, then you win $2; if they are different colors, then you win −$1.00. (That is, you lose $1.00.) Calculate
a) The probability that you win in the 1st round
b) The expected value of the amount you win in the 1st round.
c) Now if the 2 marbles withdrawn in the 1st round are eliminated from the box. And the box is not
refilled, i.e. now the box only has 8 marbles. Find the probability that you win in the 2nd round
when the same rule as the 1st round is applied to the 2nd round. Question 6: (10 pts)
A coin is tossed 4 times. For the 1st time that the head appears the player will be rewarded one. For the 2nd
time that the Head appears the total reward will be increase by 2. For the 3rd time that the Head appears
the total reward will be added by 3. The same rule is applied for the 4th. Given that the probability of Head appearance is 0.5
a) Find the expected reward that the player received. GOOD LUCKS!
Statistics for Business- Midterm Exam 6,Apr, 2019 2