Question

The mean life expectancy of a certain type of light bulb is 945 hours with a standard deviation of 21 hours. What is the approximate standard deviation of the sampling distribution of the mean for all samples with n

Answer 1

The approximate standard deviation of the sampling distribution of the mean for all samples of size n is
`s = (\sigma)/(√(n)) = (21)/(√(n))`

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.

The mean life expectancy of a certain type of light bulb is 945 hours with a standard deviation of 21 hours

This means that
`\mu = 945, \sigma = 21`.

What is the approximate standard deviation of the sampling distribution of the mean for all samples of size n?

`s = (\sigma)/(√(n)) = (21)/(√(n))`

The approximate standard deviation of the sampling distribution of the mean for all samples of size n is
`s = (\sigma)/(√(n)) = (21)/(√(n))`