International University - VNUHCM
School of Industrial Engineering and Management (IEM) ----------------- Midterm Examination
Date: Tuesday, Nov 09th 2021; Duration: 120 minutes
Open book; Online, Laptops/Cell-phone/& are not allowed.
SUBJECT: Engineering Probability & Statistics (ID: IS004IU)
Approval by the School/Department Lecturer: Signature Signature Full name: Dr. Tran Duc Vi, Dr. Phan Nguyen Ky Phuc Full name: H Thß Xu n Chi Proctor 1 Proctor 2 Signature Signature Full name: Full name: STUDENT INFO Student name: Student ID:
INSTRUCTIONS: the total of point is 100 (equivalent to 30% of the course) 1. Purpose: ¥
Able to understand, calculate, and present basic statistics for a given dataset including numerical and (G1) ¥
Able to understand calculate probability and other attributes of discrete and continuous random variables (G2) ¥
Able to conduct the simple data exploration (G4)
HCMC National University Student Name: ... .
International University Student ID:
. - - - - - - - - - - - - 2.
Requirement:
¥ Discussion and material transfer are strictly prohibited.
¥ Submit your exam on Blackboard right after the exam time is over. QUESTIONS Question 1 (25 points)
Following are GPA of 20 students admitted to graduate program in School of Industrial Engineering and Management (IEM)
3.55, 3.65, 3.57, 3.83, 3.76, 3.78, 3.63, 3.88, 3.65, 3.59
3.53, 3.58, 3.65, 3.82, 3.81, 3.64, 3.57, 3.69, 3.80, 3.78
a. Represent the data in a stem and leaf plot (5 pts)
b. Calculate the same mean 㗆. (5pts)
c. Calculate the sample standard deviation s. (5pts)
d. Determine the proportion of the data values that lies within 㗆±1.5㗆 and compare with the lower
bound given by Chebyshev s inequality. (5pts)
e. Draw the box plot from the data (5pts) Question 2 (20 points)
A man has 2 coins, one is fair coin and one is 2-head coin. He randomly picks a coin and toss it.
a) Find the probability that the face up value is Head (5 pts)
b) Given the face up value is Head what is the probability that it comes from the 2-head coin?
If the result is Head he will pick an item from factory 1. If the result is Tail, he will pick an item
from factory 2. The ratios of defective item in factory 1 and 2 are 50% and 60%. (5pts)
c) Find the probability that the item he picks is defective. (5 pts)
d) Given the item he picks is defective, find the probability that this result is come from the toss of fair coin. (5pts) Question 3 (15 points)
We roll two fair 6-sided dice. Each one of the 36 possible outcomes is assumed to be equally likely.
(a) Given that the roll results in a sum of 4 or less, find the conditional probability that doubles are rolled. (5 pts)
(b) Find the probability that at least one die roll is a 5. (5 pts)
(c) Given that the two dice land on different numbers, find the conditional probability that at least one die roll is a 5. (5 pts) /3 2
HCMC National University Student Name: ... .
International University Student ID:
. - - - - - - - - - - - - Question 4 (10 points)
At beginning at each month, a store always refills its stock so that the number of TVs in the store is
equal to 6. The target for the sale man is to sell 4 TVs / month. If he can sale more than 4, he will
receive a reward of 3 for each extra TV sale. Assume that the demand of televisions in a month follows
binomial distribution with n=6, p=0.6.
a) Find the probability that sale man can have the reward. (5 pts)
b) Find the expected reward of the sale man (5 pts) Question 5 (15 points)
Assume that the number of defect screws in a box follows Poisson distribution with 㗰=2. The box will
pass the quality test if number of defect screw is smaller or equal to 3.
a) Find the probability passing the quality test of a box. (7pts)
b) In stead of checking each box, now two boxes are combined as a package. A package will
pass the quality test if number of defect screws is smaller or equal to 6. Find the probability
passing the quality test of a package. (8pts) Question 6 (15 pts)
Weekly demand for a product has a normal distribution with mean 1,500 and standard deviation of 100.
The current on hand inventory is 2,500 and no deliveries will be occurring in the next two weeks.
Assuming that the demands in different weeks are independent,
a) what is the probability that the demand in each of the next 2 weeks is less than 1,400? (7 pts)
b) What is the probability that the total of the demands in the next 2 weeks exceeds 2,000? (8 pts) - END — /3 3