Probability and statistics exercises môn Xác suất thống kê| Trường Đại học Ngoại Thương

08:33, 28/01/2026
Probability and Statistics Exercises: Solutions for 250330 & 210607 - Studocu
PROBABILITY AND STATISTICS EXERCISES
- 6.16-6.51; 6.80-6.95;
- 7.1-7.38; 7.43,44,45,46,47,49,50,53,54,55; 7.84-7.106; 7.110-7.119;
- 8.15 -8.54; 8.83-8.100
1. In a school, 48% of the students take a foreign language class and 19% of students
take both foreign language and technology. What is the probability that a student
takes technology given that the students takes foreign language?
2. The test contains 10 questions, each one with available four different answers,
among which just one is correct. To pass the test at least 5 questions must be
answered correctly. What is the probability that completely unprepared student will pass the test ?
3. In the class of 30 students, seven of them don't have done the homework. The
teacher choosed randomly 6 students. What is the chance that at least four of them have done their homework ?
4. Three shooters shoot at the same target, each of them shoots just once. The first
one hits the target with a probability of 70%, the second one with a probability
of 80% and the third one with a probability of 90%. What is the probability that
the shooters will hit the target a) at least once b) at least twice ?
5. Based on incidence rate, the following table presents the corresponding numbers per 100,000 people. Cancer Symptom Total No Yes No 99989 0 99989 Yes 10 1 11 Total 99999 1 100000 08:33, 28/01/2026
Probability and Statistics Exercises: Solutions for 250330 & 210607 - Studocu
Which can then be used to calculate the probability of having cancer when you have the symptoms:
6. A factory produces an item using three machines—A, B, and C—which account
for 20%, 30%, and 50% of its output, respectively. Of the items produced by
machine A, 5% are defective; similarly, 3% of machine B's items and 1% of
machine C's are defective. If a randomly selected item is defective, what is the
probability it was produced by machine C?
7. X is a discrete random variable. The table below defines a probability distribution for X X 0 1 2 3 P 0.17 0.14 0.36 0.33
What is the expected value of X? What is the variance value of X?
8. The random variable X is given by the following PDF. Check that this is a valid
PDF and calculate the expected, the variance, the standard deviation values of X.
9. Let X be a continuous random variable with the following
𝑓(𝑥)={𝑐𝑒−𝑥 𝑖𝑓 𝑥 ≥ 0
0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
where c is a positive constant. a. Find c.
c. Find P(110. Let X be a random variable following a normal distribution model N(10,2). a. Calculate P(X≤10). b. Calculate P(8≤X≤14). 08:33, 28/01/2026
Probability and Statistics Exercises: Solutions for 250330 & 210607 - Studocu
11. Let Z be a random variable following a standard normal distribution model.
Determine the value of x in the following cases using the table of the distribution function: a. P(Zb. P(Z>x)=0.0606. c. P(0≤Z≤x)=0.4783. d. P(−1.5≤Z≤x)=0.2313. e. P(−x≤Z≤x)=0.5467.
12. It is known that the glucose level in blood of diabetic persons follows a normal
distribution model with mean 106 mg/100 ml and standard deviation 8 mg/100 ml.
a. Calculate the probability of a random diabetic person having a glucose level less than 120 mg/100 ml.
b. What percentage of persons have a glucose level between 90 and 120 mg/100 ml?
13. It is known that the cholesterol level in males 30 years old follows a normal
distribution with mean 220 mg/dl and standard deviation 30 mg/dl. If there are
20000 males 30 years old in the population,
a. How many of them have a cholesterol level between 210 and 240 mg/dl?
b. If a cholesterol level greater than 250 mg/dl can provoke a thrombosis, how
many of them are at risk of thrombosis?
c. Calculate the cholesterol level above which 20% of the males are?
14. In a population with 40000 persons, 2276 have between 0.8 and 0.84 milligrams of
bilirubin per deciliter of blood, and 11508 have more than 0.84. Assuming that the
level of bilirubin in blood follows a normal distribution model,
a. Calculate the mean and the standard deviation.
b. How many persons have more than 1 mg of bilirubin per dl of blood?
15. . If 95% of households have a TV and 8 houses are surveyed, what is the probability that more than 6 have a TV?
16. A manufacturer knows that an average of 1 out of 10 of his products are faulty. 08:33, 28/01/2026
Probability and Statistics Exercises: Solutions for 250330 & 210607 - Studocu
What is the probability that a random sample of 5 articles will contain: a. No faulty products b. Exactly 1 faulty products c. At least 2 faulty products
d. No more than 3 faulty products
17. Complete the table for the following binomial distributions: standard n p mean Variance deviation a 50 0.5 b 20 5 c 0.4 100
where n = number of trials and p = probability of a success.
18. The probability that cars passing a speed camera are speeding is 0.23. If 750 cars
pass the camera, how many of the cars would you expect to be speeding and what
would be the standard deviation? 08:33, 28/01/2026
Probability and Statistics Exercises: Solutions for 250330 & 210607 - Studocu