A tire manufacturer claims (based on years of experience with its tires) that the mean mileage is

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A tire manufacturer claims (based on years of experience with its tires) that the mean mileage is 35,000 miles and the standard deviation is 5000 miles. A consumer agency randomly selects 100 of these tires and finds a sample mean of 31,000.

Should the consumer agency doubt the manufacturer’s claim?

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