statistics fall2013 - midterm sample test 05

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

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---O0O--- MID-TERM EXAMINATION

SAMPLE TEST 05 DURATION: 100 MINUTES

STUDENT ID: NAME:

DATE:

INSTRUCTIONS:

1. This is an open book examination. Answer multiple choice questions in exam question paper, answer writing in answer sheets provided.

2. Calculator and dictionary are allowed. 3. Discussion and material transfer are strictly prohibited.

PART I: Multiple Choice Questions (36%)

Use the following problem to answer next 2 questions:

A Professor wants to establish a finance group of 5 members. Members of the group are selected from 6 women and 9 men.

1. How many ways to select a group consists of 3 women and 2 men? ________________________________________________________________________________________________________________________________________________________

2. What is the probability that the group would consist of 3 women and 2 men? ________________________________________________________________________________________________________________________________________________________

Use the following to answer next 3 questions:

The test scores for 15 students in a given class are as follow:

40, 49, 56, 62, 65, 70, 70, 72, 75, 78, 78, 82, 84, 85, 90, 67, 47, 75, 81, 80, 77, 70

3. The mean value of the test score is: ____________

4. Verify Chebyshev’s theorem using the above data: ________________________________________________________________________________________________________________________________________________________

5. Briefly verify Empirical rule using the above data: ________________________________________________________________________________________________________________________________________________________


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Use the following data for the next 3 questions:

Suppose a study of speeding violations and drivers who use car phones produced the following fictional data:

Speeding violation No speeding violation

Car phone user 63 167

Not a car phone user 89 231

6. What is the probability that a selected driver is not a car phone user and has no speeding violation? a) 0.724 b) 0.582 c) 0.58

d) 0.42 e) None of the above, specify__________

7. What is the probability that a selected driver has speeding violation given that he is a car phone user?

a) 0.414 b) 0.274 c) 0.115


8. Consider drivers who are speeding violation, what is the probability that a selected driver is a car

phone user? a) 0.2739 b) 0.4145 c) 0.3576


Use the following to answer next 2 questions:

Among the group of 20 students who registered for the statistic course, 8 of them are first-year students. 5 students are randomly selected from the group.

9. What is the probability that exactly 2 of the selected students are first-year students? a) 0.1192 b) 0.3486 c) 0.3973

d) 0.3065 e) None of the above

10. What probability that at least 3 of the selected students are first-year students?

a) 0.2962 b) 0.2348 c) 0.3973

d) 0.2587 e) None of the above

Use the following data to answer the next 4 questions:

The sample data is given: 33, 36, 37, 44, 52, 67, 69, 73, 78, 85, 96, 102, 110, 117


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11. Median of the above data is: a) 67 b) 71 c) 64

d) 98 e) None of the above

12. Treat the above data as a sample, its variance is:

a) 806.56 b) 788.857 c) 800.40

d) 761.76 e) None of the above, specify _____

13. The 55th percentile is:

a) 72.1 b) 69.3

c) 71.4 d) 73.75

e) None of the above, specify _____

14. The IQR (Inter-Quartile Range) is: a) 42.75 b) 75.6 c) 57.6

d) 82.4 e) None of the above, specify _____

15. An experienced business-school graduate has a 75% probability of getting a particular job. An

inexperienced business-school graduate has a 40% chance of getting the same job. 60% of business-school graduates are inexperienced. If the job is offered to a business-school graduate, what is the probability that the person was inexperienced? a) 0.24 b) 0.555 c) 0.667

d) 0.444 e) None of the above, specify_____

Use the following data for the next 3 questions:

An Indian company offers production of ancient furniture pieces, which have become popular in recent years. The following table gives the probability distribution of the number of Roman tables sold per day at a particular Bombay store.

Number of tables Probability

0 0.07

1 0.12

2 0.16

3 0.21

4 0.25


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5 0.10

6 0.05

7 0.04

16. The expected value and standard deviation of the number of tables sold per day is: a) 3.15 and 1.728 b) 3.15 and 2.988 c) 3.13 and 3.073

d) 3.13 and 1.753 e) None of the above, specify__________

17. Find the probability that the number of tables sold per day is at least 3 and less than 6:

a) 0.35 b) 0.61 c) 0.56


18. Assume that the number of tables sold each day is independent. Find the probability that the number

of tables sold per day is at least 2 and less than 5 for 3 consecutive days: a) 0.62 b) 0.238 c) 0.373


PART II (64 %)

Question 1: Given a set of data: 113, 119, 123, 128, 128, 134, 139, 147, 165, 168, 172, 176, 181, 184, 188, 193, 196, 200, 205, 230.

a. What is the mean and the standard deviation of this sample? b. Find the 1st, 2nd, 3rd quartiles and 68th percentile. c. Construct the box plot for this data set. Interpret your findings. Question 2: A bank has developed a set of criteria for evaluating distressed credit of company. Companies that passed the test will go bankrupt (non-survivor) with probability 0.4. There are 55% of the companies passed the test. The probability that a company did not pass the test will subsequently survive is 0.10 a. What is the probability that a random company will survive (not going to bankrupt) ? b. A random survived company is selected, what is the probability that company passed the test? c. What is the probability that a company is a non-survivor, given that it passed the test? Is the test

effective?

Question 4:


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Consider two boxes, the first contains 2 white and 5 black balls, the second contains 5 white and 6 black balls. We flip a fair coin and then draw a ball from the first box or the second box depending on whether the outcome was head or tail.

a. What is the conditional probability that a selected ball from the first box is black? What is the probability that a selected ball is a black ball?

b. Given that a white ball was selected, what is the conditional probability that the outcome of the toss was head?

Question 5:

In a factory, the number of defective items produced per hour has the following distributions:

Number of defective items Probability

1 0.10

2 0.18

3 0.24

4 0.32

5 0.10

6 0.06

a. Prove that this is the probability distribution of the number of defective items. Find the cumulative distribution of the number of defective items.

b. Find the expected number and the standard deviation of the number of defective items per hour. c. Find the probability that the number of defective items will be larger than 2 and at most 5. d. Find the probability that the number of defective items will be at most 4 for 4 consecutive hours;

assume that the number of defective items each hour is independent with each other.

Question 6:

According to a survey, 40% of the women love to go shopping in Diamond Plaza, 35% of the women love to go shopping in Parkson, and 25% of the women love to go shopping in Saigon Square. If 8 women are selected randomly, what is the probability that:

a. Three of them love to go shopping in Diamond Plaza? b. At most 3 of them love to go shopping in Parkson? c. Two of them love to go shopping in Saigon Square?

GOOD LUCKS!

statistics fall2013 - midterm sample test 05

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