Applied Statistics and Probability for Engineers, 5th edition

Applied Statistics and Probability for Engineers, 5th
edition
CHAPTER 2

Section 2-1

Provide a reasonable description of the sample space for each of the random experiments in Exercises 2-1 to 2-17. There
can be more than one acceptable interpretation of each experiment. Describe any assumptions you make.

2-1. Each of three machined parts is classified as either above or below the target specification for the part. Let a and b denote
a part above and below the specification, respectively.

S  aaa , aab , aba , abb , baa , bab , bba , bbb 

2-2. Each of four transmitted bits is classified as either in error or not in error.

Let e and o denote a bit in error and not in error (o denotes okay), respectively.
eeee , eoee , oeee , ooee ,
eeeo , eoeo , oeeo , ooeo ,
 
S  
eeoe , eooe , oeoe , oooe ,
 eeoo , eooo , oeoo , oooo 

2-3. In the final inspection of electronic power supplies, either units pass, or three types of nonconformities might occur:
functional, minor, or cosmetic. Three units are inspected.

Let a denote an acceptable power supply.
Let f, m, and c denote a power supply that has a functional, minor, or cosmetic error, respectively.
S  a , f , m , c

2-4. The number of hits (views) is recorded at a high-volume Web site in a day.

S  0,1,2,... = set of nonnegative integers

2-5. Each of 24 Web sites is classified as containing or not containing banner ads.

Let y and n denote a web site that contains and does not contain banner ads.
The sample space is the set of all possible sequences of y and n of length 24. An example outcome in the sample space is
S  yynnynyyyn nynynnnnyy nnyy 

2-6. An ammeter that displays three digits is used to measure current in milliamperes.

A vector with three components can describe the three digits of the ammeter. Each digit can be 0,1,2,...,9.
The sample space S is 1000 possible three digit integers, S  000 ,001 ,..., 999 

2-7. A scale that displays two decimal places is used to measure material feeds in a chemical plant in tons.

S is the sample space of 100 possible two digit integers.

2-8. The following two questions appear on an employee survey questionnaire. Each answer is chosen from the five point
scale 1 (never), 2, 3, 4, 5 (always).

Is the corporation willing to listen to and fairly evaluate new ideas?
How often are my coworkers important in my overall job performance?

Let an ordered pair of numbers, such as 43 denote the response on the first and second question. Then, S consists
of the 25 ordered pairs 1 1,12, . . . ,55




2-1

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2-9. The concentration of ozone to the nearest part per billion.

S  0 ,1,2,...,1E 09  in ppb.

2-10. The time until a service transaction is requested of a computer to the nearest millisecond.

S  0 ,1,2 ,...,  in milliseconds

2-11. The pH reading of a water sample to the nearest tenth of a unit.

S  1 .0 ,1 .1,1 .2 ,  14 .0

2-12. The voids in a ferrite slab are classified as small, medium, or large. The number of voids in each category
is measured by an optical inspection of a sample.

Let s, m, and l denote small, medium, and large, respectively. Then S = {s, m, l, ss, sm, sl, ….}

2-13 The time of a chemical reaction is recorded to the nearest millisecond.

S  0 ,1,2 ,...,  in milliseconds.

2-14. An order for an automobile can specify either an automatic or a standard transmission, either with or without air
conditioning, and with any one of the four colors red, blue, black, or white. Describe the set of possible orders for
this experiment.


automatic standard transmission
transmission




with air without air
without air
with air




red blue black whit red blue black whit red blue black white red blue black white
e e


2-15. A sampled injection-molded part could have been produced in either one of two presses and in any one of the eight
cavities in each press.



P RES S 1
2




C A V I TY




1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8




2-2

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2-16. An order for a computer system can specify memory of 4, 8, or 12 gigabytes and disk storage of 200, 300, or 400
gigabytes. Describe the set of possible orders.




memory
4 8 12




disk storage


200 300 400 200 300 400 200 300 400



2-17. Calls are repeatedly placed to a busy phone line until a connection is achieved.

Let c and b denote connect and busy, respectively. Then S = {c, bc, bbc, bbbc, bbbbc, …}


2-18. Three attempts are made to read data in a magnetic storage device before an error recovery procedure that
repositions the magnetic head is used. The error recovery procedure attempts three repositionings before an “abort’’
message is sent to the operator. Let

s denote the success of a read operation
f denote the failure of a read operation
S denote the success of an error recovery procedure
F denote the failure of an error recovery procedure
A denote an abort message sent to the operator

Describe the sample space of this experiment with a tree diagram.

S  s , fs , ffs , fffS , fffFS , fffFFS , fffFFFA 

2-19. Three events are shown on the Venn diagram in the following figure:




Reproduce the figure and shade the region that corresponds to each of the following events.
(a) A (b) A  B (c) A  BC (d) B  C (e) A  BC




2-3

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(a)




(b)




(c)




(d)




2-4

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