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1. Let X denote the time in hours needed to locate and correct a problem in the software that governs the timing of traffic lights in the downtown area of a large city. Assume that X is normally distributed with mean 10 hours and variance 9. a. Find the probability that the next problem will require at most 15 hours to find and correct. b. The fastest 5% of repairs take at most how many hours to complete?

1. Let X denote the time in hours needed to locate and correct a problem in the software that governs the timing of traffic lights in the downtown area of a large city. Assume that X is normally distributed with mean 10 hours and variance 9. a. Find the probability that the next problem will require at most 15 hours to find and correct. b. The fastest 5% of repairs take at most how many hours to complete?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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1. Let X denote the time in hours needed to locate and correct a problem in the software that governs the timing of traffic lights in the downtown area of a large city. Assume that X is normally distributed with mean 10 hours and variance 9. a. Find the probability that the next problem will require at most 15 hours to find and correct. b. The fastest 5% of repairs take at most how many hours to complete? 2. In an automobile plant two tasks are performed by robots. The first entails welding two joints; the second, tightening three bolts. Let X denote the number of defective welds and Y the number of improperly tightened bolts produce per car. Table 1: x/y 2 3 .840 .030 .020 .010 .060 .010 .008 .002 2 .010 .005 .004 .001 Use table 1 to find each of these probabilities, a. The probability that exactly two defective welds and one improperly tightened bolt will be produced by the robots. b. The probability that at least one defective weld and at least one improperly tightened bolt will be produced. c. The probability that at most one defective weld will be produced. 3. The two most common type of errors made by programmers are syntax errors and errors in logic. For a simple language such as BASIC the number of such errors is usually small. Let X denote the number of syntax errors and Y the number of errors in logic made on the first run of a BASIC program. Assume that the joint density for (X,Y) is as shown in table 2: x/y 1 2 3 400 .100 .020 .005 300 .040 .010 .004 .040 .010 .009 .003 3 .009 .008 .007 .003 4 .008 .007 .005 .002 .002 .005 .002 .001 a. Find the probability that a randomly selected program will have neither of these types of error. b. Find the probability that a randomly selected program will contain at least one syntax error and at most one error of logic. c. Find the marginal densities for X and Y d. Find the probability that a randomly selected program contains at least two syntax errors. e. Find the probability that a randomly selected program contains one or two errors in logic.
Transcribed Image Text:1. Let X denote the time in hours needed to locate and correct a problem in the software that governs the timing of traffic lights in the downtown area of a large city. Assume that X is normally distributed with mean 10 hours and variance 9. a. Find the probability that the next problem will require at most 15 hours to find and correct. b. The fastest 5% of repairs take at most how many hours to complete? 2. In an automobile plant two tasks are performed by robots. The first entails welding two joints; the second, tightening three bolts. Let X denote the number of defective welds and Y the number of improperly tightened bolts produce per car. Table 1: x/y 2 3 .840 .030 .020 .010 .060 .010 .008 .002 2 .010 .005 .004 .001 Use table 1 to find each of these probabilities, a. The probability that exactly two defective welds and one improperly tightened bolt will be produced by the robots. b. The probability that at least one defective weld and at least one improperly tightened bolt will be produced. c. The probability that at most one defective weld will be produced. 3. The two most common type of errors made by programmers are syntax errors and errors in logic. For a simple language such as BASIC the number of such errors is usually small. Let X denote the number of syntax errors and Y the number of errors in logic made on the first run of a BASIC program. Assume that the joint density for (X,Y) is as shown in table 2: x/y 1 2 3 400 .100 .020 .005 300 .040 .010 .004 .040 .010 .009 .003 3 .009 .008 .007 .003 4 .008 .007 .005 .002 .002 .005 .002 .001 a. Find the probability that a randomly selected program will have neither of these types of error. b. Find the probability that a randomly selected program will contain at least one syntax error and at most one error of logic. c. Find the marginal densities for X and Y d. Find the probability that a randomly selected program contains at least two syntax errors. e. Find the probability that a randomly selected program contains one or two errors in logic.
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