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Edition 4 Exercise STAT 601

# Edition 4 Exercise STAT 601 - 28 CHAPTER 2 PROBABILITY...

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Unformatted text preview: 28 CHAPTER 2 PROBABILITY When probability is discussed in this chapter, the probability of an event is determined as the ratio ,3 of the number of outcomes in the event to the number of outcomes in the sample space (for equally likely 3 outcomes). Therefore, the probability that a sample contains exactly two defective parts is 15,890,700 _ 0 535,095 — 0.034 ~ Note that this example illustrates a common distribution studied in Chapter 3 (hypergeometric distribution). EXERCISES FOR SECTION 2—1 Provide a reasonable description of the sample space for each of the random experiments in Exercises 2-1 to 2-18. There can be more than one acceptable interpretation of each experi- ment. 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. 2—2. Each of four transmitted bits is classiﬁed as either in error or not in error. 2—3. In the ﬁnal inspection of electronic power supplies, three types of nonconformities might occur: functional, minor, or cosmetic. Power supplies that are defective are further clas- siﬁed as to type of nonconformity. 2—4. In the manufacturing of digital recording tape, elec— tronic testing is used to record the number of bits in error in a 350-foot reel. 25. In the manufacturing of digital recording tape, each of 24 tracks is classiﬁed as containing or not containing one or more bits in error. 26. An ammeter that displays three digits is used to meas- ure current in milliamperes. 2—7. A scale that displays two decimal places is used to measure material feeds in a chemical plant in tons. 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 oﬁen are my coworkers important in my overall job performance? 29. The concentration of ozone to the nearest part per billion. 2‘10. The time until a service transaction is requested of a computer to the nearest millisecond. 2‘1 1. The pH reading of a water sample to the nearest tenth of a unit. 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. 2—13. The time of a chemical reaction is recorded to the nearest millisecond. 2.18. 2—14. An order for an automobile can specify either an automatic or a standard transmission, either with or without air- conditioning, and any one of the four colors red, blue, black or white. Describe the set of possible orders for this experiment. 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. 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. « 2—17. Calls are repeatedly placed to a busy phone line until a connect is achieved. In a magnetic storage device, three attempts are made to read data before an error recovery procedure that reposi- tions 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 F denote the failure of an error recovery procedure S denote the success 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. 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 {'1 B (d) (B U C)’ (e) (A F) B)’ U C (c) (AF‘IB)UC ...
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