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?
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: [tex] \frac{20\times8.1}{10\times8.1}=2 [/tex]
The distribution of the sample means of the weights of cheese wedges is multiplied by 2 in the new batches.
