Suppose that we randomly sample 40 light bulbs from a popula

Suppose that we randomly sample 40 light bulbs from a population that is skewed right with a mean of 10,000 hours and a standard deviation of 8,00 hours.  We calculate the mean lifespan from this sample and record the value.  We repeat this thousands of times.

1.   What will be the (approximate) mean of the value of the distribution of these thousands of sample light bulb lifespans?  What will be the standard deviation of the distribution of these thousands of light bulb lifespans?

Solution

Suppose that we randomly sample 40 light bulbs from a population that is skewed right with a mean of 10,000 hours and a standard deviation of 8,00 hours.  We calculate the mean lifespan from this sample and record the value.  We repeat this thousands of times.

1.   What will be the (approximate) mean of the value of the distribution of these thousands of sample light bulb lifespans?  What will be the standard deviation of the distribution of these thousands of light bulb lifespans?

The Central Limit Theorem states that regardless of the distribution of the parent population:

The mean of the population of means is always equal to the mean of the parent population from which the population samples were drawn.

The standard deviation of the population of means is always equal to the standard deviation of the parent population divided by the square root of the sample size (N).

The distribution of means will approximate a normal distribution as the size N of samples increases.

mean of the value of the distribution of these thousands of sample light bulb lifespans = 10000 hours

standard deviation of the distribution of these thousands of light bulb lifespans =800/sqrt( 1000) = 25.2982 hours