a. What are the expected value and standard deviation of the number of cars in the sample that have the defect? b. What is the (approximate) probability that at least 10 sampled cars have the defect? c. What is the (approximate) probability that no sampled cars have the defect?

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Problem Statement. A notice is sent to all owners of a certain type of
automobile, asking them to bring their cars to a dealer to check for the
presence of a particular manufacturing defect. Suppose that only
0.05% of such cars have the defect. Consider a random sample of
10,000 cars.
a. What are the expected value and standard deviation of the
number of cars in the sample that have the defect?
b. What is the (approximate) probability that at least 10 sampled
cars have the defect?
c. What is the (approximate) probability that no sampled cars have
the defect?
Transcribed Image Text:Problem Statement. A notice is sent to all owners of a certain type of automobile, asking them to bring their cars to a dealer to check for the presence of a particular manufacturing defect. Suppose that only 0.05% of such cars have the defect. Consider a random sample of 10,000 cars. a. What are the expected value and standard deviation of the number of cars in the sample that have the defect? b. What is the (approximate) probability that at least 10 sampled cars have the defect? c. What is the (approximate) probability that no sampled cars have the defect?
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