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p63_exercises-2_8

# p63_exercises-2_8 - 3 390 of those without the brochure can...

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Unformatted text preview: , 3 390% of those without the brochure can deal with an out- j :3: Aﬁer the ﬁrst three months of mailing, 95% of the farm- 3': Scotland received the informative brochure. Compute the )1 ility that a randomly selected farmer will have enough 1 11 tion to deal effectively with an outbreak of the disease. In an automated ﬁlling operation, the probability of orrect ﬁll when the process is operated at a low speed 1s 1 When the process is operated at a high speed, the prob- . ty of an incorrect ﬁll is 0. 01. Assume that 30% of the ' 'uers are ﬁlled when the process is operated at a high 1 and the remainder are ﬁlled when the process is ted at a low speed. What is the probability of an incorrectly ﬁlled container? , fan incorrectly ﬁlled container 1s found, what 1s the prob- , ability that it was ﬁlled during the high-speed operation? 'i' ‘52. An encryption-decryption system consists of three ments: encode, transmit, and decode. A faulty encode ' ~ in 0.5% of the messages processed, transmission errors in 1% of the messages, and a decode error occurs in of the messages. Assume the errors are independent. ‘j‘What is the probability of a completely defect- free _ message? 3 What is the probability of a message that has either an '5 encode or a decode error? ' 53 It is known that two defective copies of a commer- soﬁware program were erroneously sent to a shipping lot 3 has now a total of 75 copies of the program. A sample of i.es will be selected from the lot without replacement. 3 Ifthree copies of the soﬁware are inspected, determine the ‘ probability that exactly one of the defective copies will be ,1 found. r) If three copies of the software are inspected, determine the ’ probability that both defective copies will be found. 3;) If 73 copies are inspected, determine the probability that both copies will be found. Hint: Work with the copies that 3 remain in the lot. 3154. A robotic insertion tool contains 10 primary compo- Huts T.he probability that any component fails during the is anty period 15 0. 01. Assume that the components fail o endently and that the tool fails if any component fails. 1 -at is the probability that the tool fails during the warranty ‘ 'od? >155. An e-mail message can travel through one of two ‘ er routes. The probability of transmission error in each of 1‘3'1' servers and the proportion of messages that travel each ute are shown in the following table. Assume that the ers are independent. probability of error percentage of messages server 1 server 2 server 3 server 4 x 2-8 RANDOM VARIABLES 63 (a) What is the probability that a message will arrive without error? (b) If a message arrives in error, what is the probability it was sent through route 1? 2—156. A machine tool IS idle 15% of the time. You request immediate use of the tool on ﬁve different occasions during the year. Assume that your requests represent independent events (a) What is the probability that the tool is idle at the time of all of your requests? (b) What is the probability that the machine is idle at the time of exactly four of your requests? (c) What is the probability that the tool is idle at the time of at least three of your requests? 2—157. A lot of 50 spacing washers contains 30 washers that are thicker than the target dimension. Suppose that three wash- ers are selected at random, without replacement, from the lot. (a) What is the probability that all three washers are thicker than the target? (b) What is the probability that the third washer selected is thicker than the target if the ﬁrst two washers selected are thinner than the target? (c) What is the probability that the third washer selected is thicker than the target? 2—158. Continuation of Exercise 2-157. Washers are se- lected from the lot at random, without replacement. (a) What is the minimum number of washers that need to be selected so that the probability that all the washers are thinner than the target is less than 0.10? (b) What is the minimum number of washers that need to be selected so that the probability that one or more washers are thicker than the target is at least 0.90? 2—159. The following table lists the history of 940 orders for features in an entry-level computer product. extra memory no yes optional high- no 5 14 68 speed processor yes 1 12 246 Let A be the event that an order requests the optional high- speed processor, and let B be the event that an order requests extra memory. Determine the following probabilities: (a) P(A U B) (b) P(A H B) (c) P(A’ UB) (d) P(A’ﬂB’) (e) What is the probability that an order requests an optional high-speed processor given that the order requests extra memory? (1) What is the probability that an order requests extra mem- ory given that the order requests an optional high-speed processor? 2-160. The alignment between the magnetic tape and head in a magnetic tape storage system affects the performance of the system. Suppose that 10% of the read operations are _ute1 30 0.01 0.015 ,' ute 2 70 0.02 0.003 ...
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