Question

The distribution of actual weights of 8-ounce wedges of cheddar cheese produced at a dairy is normal with mean 8.1 ounces and standard deviation 0.2 ounces. a sample of 10 of these cheese wedges is selected. the company decides instead to sample batches of 20 cheese wedges, and the sampling is repeated every time workers start a new shift at the dairy. how will the distribution of the sample means of the weights of cheese wedges change from the previous batches, which only contained 10 samples?

Answer 1

The mean of the weight is 8.1 ounces. 
So the means of the distribution of 10 sample will be 10*8.1.
And the mean of 20 cheese wedges is again 20*8.1. 
(The mean of the addition of two normal law is the sum of the 
mean of each law)
Divide the above two numbers: $\frac{20\times8.1}{10\times8.1}=2$

The distribution of the sample means of the weights of cheese wedges is multiplied by 2 in the new batches.