A manufacturer of large kitchen appliances keeps track of the costs of warranty claims. Management suspects that 75% of all warranty claims are invalid, 20% cost the company less than $500, and 5% cost the company more than $500. To investigate this belief, a random sample of 80 warranty claims is selected from their vast records of past warranty claims. The management would like to know if the distribution of claim results differs from what they suspect.

Are the conditions for inference met?

A. No, the random condition is not met.

B. No, the 10% condition is not met.

C. No, the Large Counts condition is not met.

D. Yes, all of the conditions for inference are met.

The first condition is the random condition. For inference to be valid, the sample of 80 warranty claims should be randomly selected from the vast records of past warranty claims. However, it is explicitly stated that the sample is not random, indicating that this condition is not met.

The second condition is the 10% condition. It requires that the sample size (80 warranty claims) is less than 10% of the population size. Since the size of the population of past warranty claims is not provided, we cannot determine if this condition is met or not.

The third condition is the Large Counts condition. This condition states that both the expected number of successes (valid warranty claims) and failures (invalid warranty claims) should be at least 10. Without knowing the total number of warranty claims or the specific proportions, we cannot determine if this condition is met.

Therefore, based on the information provided, we can conclude that the conditions for inference are not met. Further analysis or additional information would be required to assess the distribution of claim results and investigate whether it differs from the suspected proportions.

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