Annual income: The mean annual income for people in a certain city (in thousands of dollars) is 41, with a standard deviation of 28. A pollster draws a sample of 92 people to interview.

By the Central Limit Theorem, the distribution of the sample means is approximately normal with mean 41 and standard deviation 2.92, in thousands of dollars.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 41, standard deviation of 28:

This means that

Sample of 92:

This means that

Distribution of the sample means:

By the Central Limit Theorem, the distribution of the sample means is approximately normal with mean 41 and standard deviation 2.92, in thousands of dollars.

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