Question

A company has machinery calibrated for a certain widget to manufacture the product so that all of the products will average out to a mean weight of 7 grams and a standard deviation of 2 grams. What would you expect as a sampling distribution if you were to take repeated samples of 100 widgets?

Answer 1

By the Central Limit Theorem, the sampling distribution of repeated samples of 100 widgets would be approximately normal with mean 7 grams and standard deviation 0.2 grams.

Explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean
`\mu` and standard deviation
`\sigma`, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
`\mu` and standard deviation
`s = (\sigma)/(√(n))`.

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

Mean weight of 7 grams and a standard deviation of 2 grams.

This means that
`\mu = 7, \sigma = 2`

Sample of 100:

This means that
`n = 100, s = (2)/(√(100)) = 0.2`

What would you expect as a sampling distribution if you were to take repeated samples of 100 widgets?

By the Central Limit Theorem, the sampling distribution of repeated samples of 100 widgets would be approximately normal with mean 7 grams and standard deviation 0.2 grams.