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(a) A new car model has a design fault, as a result of which 10% of production cars have a particular ignition problem. Engineers have come up with a modification which they hope will end the difficulty, and a pilot run of 30 cars is manufactured using the modified design. State and briefly justify a distribution you might consider using to model the number of cars X in this pilot run with the ignition problem. (b) Suppose that the modification has no effect on the problem. Using your model, find Pr(X=0) and Pr(X = 1). If in fact no cars have the problem, would the manufacturer be justified in concluding that the change has definitely improved the situation? (c) Suppose now that the problem occurs in only 1% of cars manufactured in the modified way. Estimate the probability that in the first 500 cars there are no more than two still with the problem. (d) Later, the manufacturer claims that as a result of the modification the problem occurs in

(a) A new car model has a design fault, as a result of which 10% of production cars have a particular ignition problem. Engineers have come up with a modification which they hope will end the difficulty, and a pilot run of 30 cars is manufactured using the modified design. State and briefly justify a distribution you might consider using to model the number of cars X in this pilot run with the ignition problem. (b) Suppose that the modification has no effect on the problem. Using your model, find Pr(X=0) and Pr(X = 1). If in fact no cars have the problem, would the manufacturer be justified in concluding that the change has definitely improved the situation? (c) Suppose now that the problem occurs in only 1% of cars manufactured in the modified way. Estimate the probability that in the first 500 cars there are no more than two still with the problem. (d) Later, the manufacturer claims that as a result of the modification the problem occurs in

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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(a) A new car model has a design fault, as a result of which 10% of production cars have a particular ignition problem. Engineers have come up with a modification which they hope will end the difficulty, and a pilot run of 30 cars is manufactured using the modified design. State and briefly justify a distribution you might consider using to model the number of cars X in this pilot run with the ignition problem. (b) Suppose that the modification has no effect on the problem. Using your model, find Pr(X=0) and Pr(X= 1). If in fact no cars have the problem, would the manufacturer be justified in concluding that the change has definitely improved the situation? (c) Suppose now that the problem occurs in only 1% of cars manufactured in the modified way. Estimate the probability that in the first 500 cars there are no more than two still with the problem. (d) Later, the manufacturer claims that as a result of the modification the problem occurs in only 0.5% of cars. An independent survey of 500 cars finds that 6 have the problem. Is the manufacturer's claim reasonable?
Transcribed Image Text:(a) A new car model has a design fault, as a result of which 10% of production cars have a particular ignition problem. Engineers have come up with a modification which they hope will end the difficulty, and a pilot run of 30 cars is manufactured using the modified design. State and briefly justify a distribution you might consider using to model the number of cars X in this pilot run with the ignition problem. (b) Suppose that the modification has no effect on the problem. Using your model, find Pr(X=0) and Pr(X= 1). If in fact no cars have the problem, would the manufacturer be justified in concluding that the change has definitely improved the situation? (c) Suppose now that the problem occurs in only 1% of cars manufactured in the modified way. Estimate the probability that in the first 500 cars there are no more than two still with the problem. (d) Later, the manufacturer claims that as a result of the modification the problem occurs in only 0.5% of cars. An independent survey of 500 cars finds that 6 have the problem. Is the manufacturer's claim reasonable?
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