statistics fall2013 - midterm sample test 01

Vietnam National University – HCM Academic Year 2013 – 2014, Semester 01 International University Course: Statistics for Business

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---OOO--- MID-TERM EXAMINATION

SAMPLE TEST 01

Duration: 180 Minutes

Student ID: Name:

Date:

INSTRUCTIONS 1. This is an open book examination. 2. Calculator is allowed. 3. Discussion and material transfer are strictly prohibited.

PART I : (Please answer on the QUESTION SHEET)

1. The prices of product XY in a shop ranged as follows: 0.89, 0.95, 1.25, 1.36, 1.49, 1.65, 1.79, 1.89, 1.99. What are the upper and lower quartiles of prices for this product

a. 1.79; 1.25 b. 1.72, 1.10

c. 1.84, 1.17 d. 1.21, 0.74

e. None of above: ……… (Specified)

2. A new medicine has an 75% success rate. Six patients are treated with it. What is the

probability that at least four are cured with this new medicine?

a. 0.8306 b. 0.9130

c. 0.7443 d. None of above: ……… (Specified)

Use the following data to answer the next 2 questions

From a group of six men and four women, a committee of four is to be chosen.

3. What is the probability that this committee consists of exactly two men and two women?

a. 0.100 b. 0.4286

c. 0.7143 d. None of above: ……… (Specified)

4. What is the probability that this committee will consist of all men?

a. 0.0714 b. 0.100

c. 1 d. None of above: ……… (Specified)


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5. Let X be a normally distributed random variable with mean 100 and standard deviation 20. Find two values, a and b, symmetric about the mean, such that the probability of the random variable being between them is 0.99.

a. 48.5, 151.5 b. 90.5, 105.9

c. 80.2, 119.8 d. None of above: ……… ……….(Specified)

Use the following data to answer the next 3 questions The number of computer terminals in use on a given night at Bentley College is a random variable, X, with the following probability distribution:

X P(x)

0 0.1

1 0.2

2 0.4

3 0.2

4 0.1

6. The average number of terminals in use is a. 1 b. 2

c. 3 d. None of above: ……………….. (Specified)

7. The standard deviation is: a. 1.0955 b. 1.2374

c. 1 d. None of above:…………….(Specified)

8. What is the percentage of at least 2 computer terminals in use: a. 30% b. 70%

c. 90% d. None of above:…………….(Specified)

9. A professor grades his students on a normal distribution, with mean at 75 and standard deviation of 15. If there are 39 students in his class, how many score between 80 and 90?

a. 21 b. 8


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c. 13 d. None of above:…………….(Specified)

10. A grocery store has a mean accounts receivable of $264, with a standard deviation of $55. The accounts receivable are approximately normally distributed. Find the value such that 45% of all the accounts exceed this value. That is, find x0 such that: P(X > x0) = 0.45

a. $257.13 b. $309.00

c. $270.88 d. None of above:…………….(Specified)

11. Suppose that an instructor gives an exam. This instructor wants to give those students in the top 2.5% an A on this exam. What will the cutoff be for an A, if the average score on this exam is 80, with a standard deviation of 5 ? Assume that it follows normal distribution.

a. About 90 b. About 85

c. About 82 d. None of above:…………….(Specified)

Use the following data to answer the next 2 questions Suppose there are 16 major computer companies in the United States and that 10 are located in California’s Silicon Valley. Three computer companies are selected randomly from the entire list. 12. What is the probability that one or more of the selected companies are located in the Silicon

Valley.

a. 0.9643 b. 0.2679

c. 0.3036 d. None of above:…………….(Specified)

13. What is the probability that exactly two of the selected companies are located in the Silicon Valley

a. 0.7857 b. 0.6964


14. A study conducted by ABC Organization found that 75% of all finacial consumers are very satisfied with their primary finacial institution. Suppose 24 financial consumers are sample randomly. What is the probability that exactly 11 of 24 are very satisfied with their primary financial institution.


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a. 0.0016 b. 0.0031


15. A tire manufacturer believes that their tires will last an average of 48,000 miles, with standard deviation of 2,000 miles. What is the probability that one of these tires, chosen at random, will last at least 50,000 miles. Assume that it follows normal distribution.

a. 0.6587 b. 0.1587


Use the following data to answer the next 4 questions The number of motorcycles produced per month is a random variable with the following probability distribution:

X P(X)

4 0.25

5 0.18

6 0.12

7 0.1

8 0.25

9 0.1

16. The probability that the number of motorcycles produced next month will be between 5 and 8 (both inclusive)

a. 0.43 b. 0.65


17. If the fixed monthly cost is $30,000 and the additional cost is $2700 per motorcycle. Find the monthly expected cost of the operation.

a. $ 46,794 b. $52,028

c. $ 36,987 d. None of above:…………….(Specified)

18. The variance of monthly cost of operation is:


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a. 2,490,178.681 b. 22,829,379.56

c. 62,875.5625 d. None of above:…………….(Specified)

19. The standard deviation

a. 1578.03 b. 250.75


The following data set is used for the next 4 questions 52, 90, 88, 61, 75, 82, 75, 83, 88, and 86

20. The median of this data set is

a. 78 b. 88

c. 82.5 d. None of above: …………

21. The IQR of this data set is

a. 75 b. 87.5


22. The 80th percentile of this data set is

a. 88 b. 90

c. 86 d. None of above: …………

23. What is the percentile of the value 82?

a. 44th b. 50th

c. 60th d. None of above: …………

The following data set is used for the next 3 question 212, 213, 214, 225, 236, 247, 258, 266, 279, 252, 223, 224, and 252

24. The mean of this data set is

a. 238.54 b. 236



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25. The standard deviation of this sample is a. 21.99 b. 483.77


26. Based on Chebyshev’ theorem, what are the bounds should include at least 80% of property

valuations? Answer:………………….

The following data is used for the next 3 question There are 2 milling machines A and B in a workshop. Machine A breaks down with the probability 0.25, and machine B breaks down with the probability 0.4. The probability that two machines break down is 0.2.

27. What is the probability that 2 machines work?

a. 0.65 b. 0.45


28. Given that machine A breaks now, what is the probability that machine B also breaks?

a. 0.65 b. 0.45


29. Given that machine B is working now, what is the probability that machine A is also

working?

a. 0.65 b. 0.55


30. There are 10 engineers in XYZ Company. Three of them graduated from MIT. How many ways can a group of 4 chosen engineers include 2 from MIT?

Answer:………

31. If probability of event A is 0.3, probability of event B is 0.5 and the probability of the union of A and B is 0.65 then

a. A and B are mutually exclusive b. A and B are dependent

c. A and B are independent d. None of above: …………


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32. In this term, student A takes 5 courses. The probability to fail one course is 0.4. What is the probability that A will pass all courses? Assume that passing a course is independent of each other. Answer:………

Use the following data to answer the next 4 questions:

The sample data is given:

21.2, 17.5, 20.9, 18, 22.6, 20, 14.3, 17.2, 29.6, 30.4, 25.5, 22.7

33. Mean of the above data is:

a. 20.4 b. 21.7

c. 22.5 d. 23.1


34. Its variance is:

a. 25.4 b. 26.5

c. 24.0 d. 27.7


35. The 86th percentile is:

a. 27.6 b. 26.5

c. 25.5 d. 27.4


36. The IQR (Inter-Quartile Range) is:

a. 5.5 b. 8.5

c. 7.0 d. 4.6



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PART II: (Please answer on ANSWER SHEET)

Question 1: According to the U.S Bureau of the Census, approximately 7.2% of all worker in Jackson, Mississippi, are unemployed. In conducting a random survey in Jackson. What is the probability of getting 3 or fewer unemployed workers in a sample of 22? Question 2: Catalog Age list the top 20 U.S firms in annual catalog sales. Of these 20 firms on the list, nine are in some type of computer-related business. Suppose 5 firms are randomly selected.

a. What is the probability that none of the firms are in some type of computer-related business?

b. What is the probability that all five firms are in some type of computer-related business? c. What is the probability that two or more firms are in some type of computer-related

business? Question 3: The U.S. Environmental Protection Agency publishes figures on solid waste generated in the United States. One year, the average number of waste generated per person per day was 4.28 pounds. Suppose the daily amount of waste generate per person is normally distributed with a standard deviation of 2.05 pounds. Of the daily amount of waste generated per person, 75.8% would be greater than what amount? Question 4: Assume that the data are normally distributed. The standard deviation of the distribution is 27.15 and 92.36% of the value are less than 156. What is the value of ? Question 5:

There are about 80% of people in this city play football. 90% of people go to the stadium for watching a football match at weekend. There are 75% also play football and watch football match at weekend. a. What is the percentage of people dislike football (neither playing football nor watch a

football match)? b. Given that a chosen people watch football match, what is the probability that people also

play football? c. Given that a chosen people do not watch football match, what is the probability that

people play football? d. Given that a chosen people watch football match, what is the probability that people do

not play football?


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Question 6: The data set is given below 125, 127, 129, 134, 133, 135, 124, 129, 140, 133, 130, 129, 127, 130, 131, 133, 132, 124, 139, 137.

a. What is the mean and standard deviation of this sample? b. Find the median, the 1st quartile, 3rd quartile and the IQR. c. Find the 70% percentile of this data. d. Find the rank of the value 128. e. Construct a Box plot for this data set.

Question 7: The following table gives the number of male and female in an area by education category

Male Female

Primary school 325 330

Secondary school 275 250

High school 200 205

Under graduated 150 140

Post graduated 55 40

a. Suppose a person is randomly selected. What is the probability that person is a male? b. What is the probability that a person, who is a female, is under-graduated? c. What is the probability that a person, who is not post graduated, is a female? d. Let A is the event that a person is under-graduated; B is the event that a person is a

female. What is the relation of A and B: mutually exclusive, independent or both? GOOD LUCK!

statistics fall2013 - midterm sample test 01

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