Question

The chefs at a local pizza chain, strive to maintain the suggested size of their 16-inch pizzas. Despite their best efforts, they are unable to make every pizza exactly 16 inches in diameter. The manager has determined that the size of the pizzas is normally distributed with a mean of 16 inches and a standard deviation of 0.8 inch.

a. What are the expected value and the standard error of the sample mean derived from a random sample of 2 pizzas?

b. What are the expected value and the standard error of the sample mean derived from a random sample of 4 pizzas?

c. Compare the expected value and the standard error of the sample mean with those of an individual pizza.

Answer 1

Solution:

a. What are the expected value and the standard error of the sample mean derived from a random sample of 2 pizzas?

Answer: The expected value is given below:

The standard error of the sample mean derived from a random sample of 2 pizzas is:

rounded to 2 decimal places

b. What are the expected value and the standard error of the sample mean derived from a random sample of 4 pizzas?

Answer:

The expected value is given below:

The standard error of the sample mean derived from a random sample of 4 pizzas is:

c. Compare the expected value and the standard error of the sample mean with those of an individual pizza.

Answer: The expected value of the sample means is the same as that of the expected value of an individual pizza. While the standard error of the sample means is less than the standard error of an individual pizza. The standard error of the sample means decreases as the sample size increases.