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Midterm Exam - Probability and Statistics Theory, Exams of Mathematical Statistics

A midterm exam for a probability and statistics theory course at the foreign trade university, hcmc campus. The exam covers various topics in probability and statistics, including conditional probability, poisson distribution, normal distribution, and combinatorics. The exam consists of 6 questions, each testing the students' understanding of the theoretical concepts and their ability to apply them to real-world scenarios. Detailed information about the exam, such as the course code, academic year, exam duration, and the marking scheme. This exam could be useful for university students studying probability and statistics, as it offers practice questions and an opportunity to assess their knowledge of the subject matter. The document could also be valuable for instructors in designing similar exams or for students seeking to review and prepare for their own probability and statistics exams.

Typology: Exams

2023/2024

Uploaded on 05/26/2024

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Midterm Exam – Class code 125
FOREIGN TRADE UNIVERSITY
HCMC CAMPUS
Deapartment of Basic Science
_________________________
MIDTERM EXAM QUESTIONS
Probability and Statistics Theory
__________________________________
Semester: 1 Academic year: 2023 – 2024
Full-time/Part-time: Full-time
Class code: 125
Form of Exam: Written Exam
Duration: 60 minute (excluding paper distribution time)
Question 1. (2 marks) Given that 10% of the people who come into the showroom and talk to a
salesperson will purchase a car. To increase the chances of success, you propose to offer a free
dinner with a salesperson. The project is conducted, and 40% of the people who purchased cars
had a free dinner. In addition, 10% of the people who did not purchase cars had a free dinner.
a. (1 mark) What is the probability that a person will have a free dinner?
b. (0,5 marks) What is the probability that a person who accepts a free dinner will purchase a
car?
c. (0,5 marks) What is the probability that a person who does not accept a free dinner will
purchase a car?
Question 2. (2 marks) A contractor estimates the probabilities for the number of days required
to complete a certain type of construction project as follows:
Time (days) 1 2 3 4 5
Probability 0,05 0,20 0,35 0,30 0,1
a. (1 mark) What is the probability that a randomly chosen project will take less than 3 days to
complete?
b. (1 mark) The contractor’s project cost is made up of two parts—a fixed cost of $20,000, plus
$2,000 for each day taken to complete the project. Find the mean and standard deviation of
total project cost.
Question 3. (1 mark) The number of accidents in a production facility has a Poisson
distribution with a mean of 2.6 per month. For a given month what is the probability there will
be more than 3 accidents?
1
PAPER NO.: 1
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Midterm Exam – Class code 125 FOREIGN TRADE UNIVERSITY HCMC CAMPUS Deapartment of Basic Science _________________________

MIDTERM EXAM QUESTIONS

**Probability and Statistics Theory


Semester: 1 Academic year: 2023 – 2024 Full-time/Part-time: Full-time Class code: 125 Form of Exam: Written Exam Duration: 60 minute** (excluding paper distribution time) Question 1. (2 marks) Given that 10% of the people who come into the showroom and talk to a salesperson will purchase a car. To increase the chances of success, you propose to offer a free dinner with a salesperson. The project is conducted, and 40% of the people who purchased cars had a free dinner. In addition, 10% of the people who did not purchase cars had a free dinner. a. (1 mark) What is the probability that a person will have a free dinner? b. (0,5 marks) What is the probability that a person who accepts a free dinner will purchase a car? c. (0,5 marks) What is the probability that a person who does not accept a free dinner will purchase a car? Question 2. (2 marks) A contractor estimates the probabilities for the number of days required to complete a certain type of construction project as follows: Time (days) 1 2 3 4 5 Probability 0,05 0,20 0,35 0,30 0, a. (1 mark) What is the probability that a randomly chosen project will take less than 3 days to complete? b. (1 mark) The contractor’s project cost is made up of two parts—a fixed cost of $20,000, plus $2,000 for each day taken to complete the project. Find the mean and standard deviation of total project cost. Question 3. (1 mark) The number of accidents in a production facility has a Poisson distribution with a mean of 2.6 per month. For a given month what is the probability there will be more than 3 accidents? 1

PAPER NO.: 1

Midterm Exam – Class code 125 Question 4. (2 marks) Given the density function of a random variable. a. (1 mark) Find the probability that is less than or equal to 0,3. b. (1 mark) Find the expected value and variance of. Question 5. (2 marks) It is estimated that the time that a well-known rock band, the Living Ingrates, spends on stage at its concerts follows a normal distribution with a mean of 200 minutes and a standard deviation of 20 minutes. a. (1 mark) An audience member smuggles a tape recorder into a Living Ingrates concert. The reel-to-reel tapes have a capacity of 245 minutes. What is the probability that this capacity will be insufficient to record the entire concert? b. (1 mark) The probability is 0.2 that a Living Ingrates concert will last less than how many minutes? Question 6. (1 mark) Package I has 5 products of type A, 1 product of type B. Package II has 2 products of type A, 4 products of type B. From each package, 1 product is randomly selected to deliver to the customer. Then the remaining products are put together into empty package III. If we randomly select 2 products from package III, calculate the probability that there is at least 1 type B product among the 2 selected products? 2