IXL - Distributions of sample means (Precalculus practice)

Samples are drawn from a population with mean 176 and standard deviation 42. Each sample has 11 randomly and independently chosen elements.

Find the mean,

𝜇

of the distribution of sample means.

𝜇

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Learn with an example

question

Samples are drawn from a population with mean 177 and standard deviation 22. Each sample has 5 randomly and independently chosen elements.

Find the mean,

𝜇

of the distribution of sample means.

𝜇

key idea

The mean of a sample from a population is called the sample

mean.

Think about samples of

randomly and independently chosen elements from the same population. A sample mean can be computed for each sample. The computed sample means are values of a random variable, usually called

The probability distribution of

depends on the sample size,

and the distribution of the population. If the population has mean

𝜇

and standard deviation

𝜎

the following are the mean and standard deviation for the distribution of sample means:

𝜇

𝜎

solution

The distribution of sample means has the same mean as the population the samples are taken from. So,

𝜇

177

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