statistics fall2013 - midterm sample test 04

7/27/2019 Statistics Fall2013 - Midterm Sample Test 04

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

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MIDTERMEXAMINATION

SAMPLETEST04Duration:

120 Minutes

Student ID:

Name:

Date:

INSTRUCTIONS:

1. This is an open book examination. No laptops, PDA.2. Use of calculator is allowed; discussion and material transfer are strictly prohibited.

PART I: Multiple-choice questions (40 points):

Use the following data for the next 2 questions:

A recent survey found that 30% of students receive their spending money from part-time jobs. 7

students are selected randomly.

1. What is the probability that there are at least 3 students who have part-time jobs?a) 0.874b) 0.126c) 0.353

d) 0.647e) None of the above, specify

____________

2. What is the probability that there are exactly 2 students who have part-time jobs?a) 0.647b) 0.552c) 0.329


____________


The test scores of 20 students in a given class are as follow:

43 89 72 53 67 54 78 57 63 58 67 61 93 81 74 76 82 91 79 80

3. How many students who have their scores greater than 75% of the whole class?


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a) 5b) 6c) 7

d) 8e) None of the above, specify

____________

4. The median of the test score is:a) 72b) 73c) 74


____________

5. The interquartile range (IQR) of the test scores is:a) 22b) 22.75c) 23


____________


A company wants to establish a working group of 7 members. Members of the group are selected

from 11 women and 13 men.

6. What is the probability that there are exactly 4 women in the group?a) 0.341b) 0.605c) 0.273


____________

7. How many ways are there to form a group of 3 women and 4 men?a) 165,120b) 117,975c) 120,120

d) 346,104e) None of the above, specify

____________

8. In a random district, the average weight of a 6th grade student is 40 kilograms, with astandard deviation of 8 kilograms. Suppose you draw a random sample of 50 students. Whatis the probability that the average weight of a sampled student will be less than 42

kilograms?

a) 0.4616b) 0.9616c) 0.0384


____________


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9. The time, in hours, that a copying machine may work without breaking down is a normallydistributed random variable with mean 525 and variance 225. The probability that the

machine will work for at least 504.75 hours without breaking down is:

a) 0.4115b) 0.0885c) 0.9641


____________


To estimate the mean height of male students on your campus, you will measure the heights of

students. Heights of people are normal distribution. You know that the standard deviation of the

heights of young men is about 4.8 inches. Suppose that the mean height of all male students is 70

inches. A random sample of 25 students is selected.

10.What is the probability that the sample mean will be less than 72 inches?a) 0.4812b) 0.0188c) 0.9812


____________

11.What is the probability that the sample mean will be between 67 and 71 inches?a) 0.8499b) 0.8508c) 0.3517


____________

12.The manager of a small computer shop buys electronic components in cartons of 12 each. Todecide if each carton is acceptable, 4 components are randomly selected and thoroughly

tested. If all 4 components are of acceptable quality then the whole batch of 12 is accepted.

If a particular carton has only 9 components of acceptable quality, what is the probability

that the sampling scheme will inadvertently accept the carton?

a) 0.7455b) 0.0182c) 0.5091


____________


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

fictional data:

Speeding violation in

the last year

No speeding violation in

the last year Total

Car phone user 45 305 350

Not a car phone user 30 420 450

Total 75 725 800

13.What is the probability that a person is a car phone user given that he/she had no speedingviolation in the last year?

a) 0.3813b) 0.9063c) 0.4206


____________

14.What is the probability that a randomly chosen person having speeding violation in the lastyear?

a) 0.0563b) 0.0938c)

0.1034


____________

15.What is the probability that a person had speeding violation in the last year given that he/sheis not a car phone user?

a) 0.0667b) 0.4c) 0.0938


____________

16.Suppose that X is normally distributed with a mean of 100 and a variance of 6400, and that arandom sample of 36 observations on X is taken. What is the probability that the sample

mean is more than 109?

a) 0.2498b) 0.2502c) 0.0002


____________


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17.A card is drawn at random from an ordinary pack of 52 cards. This card is put back to thepack and then another card is selected at random. Find the probability that at least one of the

two selected cards is a diamond.

a) 1/4b) 7/16c) 3/16

d) 6/16e) None of the above, specify

____________

18.It is known that only 20% of customers at a certain supermarket buy a particular brand ofinstant noodles. In a random sample of 20 customers of the supermarket, what is the

probability that at least one quarter of them buy that brand of noodles?

a) 0.804b) 0.370c)

0.196


____________

19.The lifespan of 100W bulbs is believed to follow a normal distribution with mean 1100 hwith standard deviation of 100 h. Find the two values, symmetric to the mean, which give

the 98% interval for the lifespan of a 100W bulb.

a) 1,096; 1,104b) 904; 1,296c) 894.6; 1,305.4

d) 867.7; 1,332.3e) None of the above, specify

____________

20.Suppose you play 8 rounds of a game in which your probability of winning a round is 0.6. Ifyou bet the same amount of money in each of the 8 rounds, what is the probability that youwill lose money, that is, win 3 or fewer rounds?

a) 0.826b) 0.124c) 0.174


____________

PART II: Writing (60 points):

Question 1 (15 points)

A car company has 3 factories. 10% of the cars are produced in factory 1, 50% in factory 2 and

the rest in factory 3. 1% of the cars produced by factory 1 are defective; 2% of the cars produced

by factory 2 are defective; and 4% from factory 3 are defective.

a) What is the probability that a randomly selected car is a defective one?


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b) What is the probability that a randomly selected car is produced by factory 3, given that itis a good one?


Consider the following data set:

50 84 57 51 70 52 52 66 93 48 80 68 42 62 89 52 90 82 73 77

a) Treat the above data set as a sample; find the mean and variance of this sample.b) Find the 70th and 85th percentiles.c) Construct the box plot for the above data set.

Question 3(12 points)

The following is the probability distribution of daily number of orders in a particular shop:

Number of orders Probability

23 0.15

24 0.2

25 0.35

26 0.2

27 0.1

a) Let X is the number of orders received daily. Find the probability: P(23 < X 26) and P(X 26).

b) Find the expected value and standard deviation of the number of orders received per day.c) Suppose that each order yields a profit of $40 and there is a fixed daily operating cost of

$500. Find the expected daily profit of the shop.


In a batch of product, produced by Company XYZ, batch sized 20, there are 5 defective

products. Random sample size 8 is selected.

a) What is probability that there are at least 3 defective products will be chosen?


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b) If a sample size 5 is selected, what is probability that at most 2 defective products will bechosen?


A soft skill club has 10 members, 7 women and 3 men. The club selected 6 members to form a

team.

a) What is the probability that there are exactly 2 women in the team?b) What is the probability there are at most 3 women will be chosen?

GOOD LUCK!

statistics fall2013 - midterm sample test 04

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