CNNBC recently reported that the mean annual cost of auto insurance is 1031 dollars. Assume the standard deviation is 200 dollars. You take a simple random sample of 68 auto insurance policies. Find the probability that a single randomly selected value is less than 977 dollars. P(X < 977) =  Find the probability that a sample of size n=68n=68 is randomly selected with a mean less than 977 dollars. P(M < 977) =

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8. CNNBC recently reported that the mean annual cost of auto insurance is 1031 dollars. Assume the standard deviation is 200 dollars. You take a simple random sample of 68 auto insurance policies.

Find the probability that a single randomly selected value is less than 977 dollars.
P(X < 977) = 

Find the probability that a sample of size n=68n=68 is randomly selected with a mean less than 977 dollars.

P(M < 977) =

 

9. The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.904 g and a standard deviation of 0.311 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 46 cigarettes with a mean nicotine amount of 0.863 g.

Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly seleting 46 cigarettes with a mean of 0.863 g or less.
P(M < 0.863 g) = 
Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Based on the result above, is it valid to claim that the amoutn of nicotine is lower?

  • No. The probability of obtaining this data is high enough to have been a chance occurrence.
  • Yes. The probability of this data is unlikely to have occurred by chance alone.



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