The weights of the population of cans of Coke are normally distributed with a mean of 12 oz and a population standard deviation of 0.13 oz. A sample of 10 cans is randomly selected from the population. (a) Find the standard error of the sampling distribution. Round your answer to 4 decimal places. .0411 (b) Using the answer from part (a), find the probability that a sample of 10 cans will have a sample mean amount of at least 12.02 oz. Round your answer to 4 decimal places. (c) Using the answer from part (a), find the probability that a sample of 10 cans will have a sample mean weight between 11.95 oz and 12.01 oz. Round your answer to 4 decimal places.
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In this case, $\sigma = 0.13$ oz and $n = 10$. Plugging in the values, we get: $$ SE = \frac{0.13}{\sqrt{10}} \approx 0.0411 $$ So, the standard error of the sampling distribution is $\boxed{0.0411}$. (b) Show more…
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The weights of the population of cans of Coke are normally distributed with a mean of 12 oz and a population standard deviation of 0.12 oz. A sample of 9 cans is randomly selected from the population. (a) Find the standard error of the sampling distribution. Round your answer to 4 decimal places. (b) Using the answer from part (a), find the probability that a sample of 9 cans will have a sample mean amount of at least 12.05 oz. Round your answer to 4 decimal places. (c) Using the answer from part (a), find the probability that a sample of 9 cans will have a sample mean weight between 11.97 oz and 12.04 oz. Round your answer to 4 decimal places.
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