##### New Member
A certain population has a bimodal distribution with a mean of 58.5 and a standard deviation of 2.5. Many samples of size 25 are randomly selected and their means calculated.

What shape would you expect the distribution of all sample means to have?
bimodal
left skewed
normal
right skewed
uniform

What values would you expect to find for the mean and the standard deviation of the sample means?
Cannot be determined
Mean 58.5, Standard Deviation 0.5
Mean 58.5, Standard Deviation 2.5
Mean 11.7, Standard Deviation 0.5
Mean 58.5, Standard Deviation 12.5

#### TheEcologist

##### Global Moderator
A certain population has a bimodal distribution with a mean of 58.5 and a standard deviation of 2.5. Many samples of size 25 are randomly selected and their means calculated.

What shape would you expect the distribution of all sample means to have?
bimodal
left skewed
normal
right skewed
uniform

What values would you expect to find for the mean and the standard deviation of the sample means?
Cannot be determined
Mean 58.5, Standard Deviation 0.5
Mean 58.5, Standard Deviation 2.5
Mean 11.7, Standard Deviation 0.5
Mean 58.5, Standard Deviation 12.5
According the the central limit theorem the sample distribution should be normal.

Here's a simulation study I run a few months back;

You can see that the sampling distribution clt.results (10000 means of random samples from the population) is normal despite the fact that the original distribution is bimodal. Red vertical line = true population mean, Green is sampling distribution mean or bootstrap esitmated mean from one sample.

The rest of the results you should be able to figure out now you know the shape is normal right?

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