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20.07.2022 - 16:38

Suppose that the number of ice cream cones eaten in a year by Americans is normally distributed and the mean number of ice cream cones Americans eat is 50 a year. Suppose that a researcher takes 1,000,000 samples of Americans, and each sample consists of

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Suppose that the number of ice cream cones eaten in a year by Americans is normally distributed and the mean number of ice cream cones Americans eat is 50 a year. Suppose that a researcher takes 1,000,000 samples of Americans, and each sample consists of 5 Americans. She asks each American how many ice cream cones they eat. She then calculates a mean for each of the 1,000,000 samples. If she added up the mean for each sample, and divided by 1,000,000, what would she get?

Answers (1)

Ellen April 8, 2023 в 04:43

The researcher would get an average of 50 ice cream cones per year, which is the mean of the original distribution. This is because the Central Limit Theorem states that the distribution of sample means from a large number of samples will be \approx imately normal, with a mean equal to the population mean. Therefore, even though each individual sample may have a different mean, the average of all the sample means will converge towards the population mean. In this case, since the population mean is 50 ice cream cones per year, the average of all the sample means will also be 50 ice cream cones per year.

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