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22:18, 27/01/2026
Đề mẫu Toán xác suất - Câu hỏi và Giải thích (MATH101) - Studocu
Câu 1. Ma trận và định thức (2 ý trong các ý, tương tự các bài tập sau)
Tài liệu 5. Ian Jacques - Mathematics for Economics and Business-Pearson
Education Limited (2018) Trang 540 Trang 543 Trang 544 Trang 562 22:18, 27/01/2026
Đề mẫu Toán xác suất - Câu hỏi và Giải thích (MATH101) - Studocu Trang 563
Find the rank of the following matrices: a. b. c. d. e.
Determine the rank of the following matrices depending on the parameter k. 22:18, 27/01/2026
Đề mẫu Toán xác suất - Câu hỏi và Giải thích (MATH101) - Studocu a. b. c.
Câu 2. Hệ phương trình tuyến tính (1 ý trong các ý sau) Trang 573
Find the general solution of the following systems of linear equations.
Determine the values of m for which the following homogeneous system has a non-trivial solution.
Câu 3. Ứng dụng hàm 1 biến số trong kinh tế và kinh doanh (1 ý trong các ý sau) 22:18, 27/01/2026
Đề mẫu Toán xác suất - Câu hỏi và Giải thích (MATH101) - Studocu
Câu 4. Phép tinh vi phân làm nhiều biến (2 ý trong các ý sau) Trang 416
Câu 5. Ứng dụng hàm nhiều biến trong kinh tế (1 ý trong các ý sau) Trang 444 22:18, 27/01/2026
Đề mẫu Toán xác suất - Câu hỏi và Giải thích (MATH101) - Studocu Trang 470
Câu 6. Normal Distribution RV (1 ý)
(1) How much money does a typical family of four spend at a McDonald’s restaurant
per visit? The amount is a normally distributed random variable with a mean of $16.40
and a standard deviation of $2.75.
a. Find the probability that a family of four spends less than $10.
b. What is the amount below which only 10% of families of four spend at McDonald’s?s
(2) Let the random variable X follow a normal distribution with = 50 and 2 = 64.
a. Find the probability that X is greater than 60.
b. Find the probability that X is greater than 35 and less than 62.
c. Find the probability that X is less than 55.
d. The probability is 0.2 that X is greater than what number? 22:18, 27/01/2026
Đề mẫu Toán xác suất - Câu hỏi và Giải thích (MATH101) - Studocu
e. The probability is 0.05 that X is in the symmetric interval about the mean between which two numbers?
(3) It is known that amounts of money spent on clothing in a year by students on a
particular campus follow a normal distribution with a mean of $380 and a standard deviation of $50.
a. What is the probability that a randomly chosen student will spend less than $400 on clothing in a year?
b. What is the probability that a randomly chosen student will spend more than $360 on clothing in a year?
c. What is the probability that a randomly chosen student will spend between $300
and $400 on clothing in a year?
d. Compute a range of yearly clothing expenditures—measured in dollars—that
includes 80% of all students on this campus? Explain why any number of such
ranges could be found, and find the shortest one.
Câu 7. (1 ý)
(1) A business school dean is contemplating proposing a change in the requirements for
graduation. At present, business majors are required to take one science course, chosen
from a list of possible courses. The proposal is that this be replaced by the requirement
that a course in ecology be taken. The business school has 420 students. In a random
sample of 100 of these students, 56 expressed opposition to this proposal. Find a 90%
confidence interval for the proportion of all the school’s students opposed to the
proposed change in requirements.
(2) An accounting firm has 1200 clients. From a random sample of 120 clients, 110
indicated very high satisfaction with the firm’s service. Find a 95% confidence interval
for the proportion of all clients who are very highly satisfied with this firm.
(3) How much do students pay, on the average, for textbooks during the first semester of
college? From a random sample of 400 students the mean cost was found to be
$357.75, and the sample standard deviation was $37.89. Assuming that the population is normally distributed. 22:18, 27/01/2026
Đề mẫu Toán xác suất - Câu hỏi và Giải thích (MATH101) - Studocu
a) Find the margin of error of a 95% confidence interval for the population mean.
b) Find a 90% confidence interval for the population mean.
(4) It is known that the amount of time needed to change the oil on a car is normally
distributed with a standard deviation of 5 minutes. The amount of time to complete a
random sample of 10 oil changes was recorded and listed here. Compute the 99%
confidence interval estimate of the mean of the population. 11 10 16 15 18 12 25 20 18 24
Câu 8. Nêu cặp giả thuyết thông kê. (1 ý)
(1) Test the hypothesis that at most 25% of all members of a population conducted no
marketing studies before opening their businesses. State the null and alternative hypotheses.
(2) A diet doctor claims that the average North American is more than 20 pounds
overweight. To test his claim, State the null and alternative hypotheses.
(3) In some states, the law requires drivers to turn on their headlights when driving in the
rain. A highway patrol officer believes that less than one-quarter of all drivers follow
this rule. To test the claim, state the null and alternative hypotheses. 22:18, 27/01/2026
Đề mẫu Toán xác suất - Câu hỏi và Giải thích (MATH101) - Studocu