The distribution of actual weights of 8-ounce wedges of cheddar cheese produced

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?

A- The distribution will still be normal, but it will be more peaked around the sample mean and the standard deviation will be larger.

B- It is not possible to tell from the information provided.

C- The shape of the distribution may change completely based on the new data.

D- The distribution will still be Normal, but it will be more peaked around the sample mean and the standard deviation will be smaller.

Explanation / Answer

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?

D- The distribution will still be Normal, but it will be more peaked around the sample mean and the standard deviation will be smaller.

mean =8.1

SD = 0.2 / srqt 10 = 0.0632

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