1. Chefs are trying to maintain the size of their pizza to be exactly 16-inch. They are not able to make every pizza exactly this size. The manager has calculated that the size of the pizzas is normally distributed with a mean of 16 inch and a standard deviation of 0.8 inch.

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

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

Hint: The Expected Value of the sample mean x equals the population mean; that is, E(x)=

The standard error of the sample mean equals the population deviation divided by the square root of the sample size.

2. Chefs are trying to maintain the size of their pizza to be exactly 16-inch. They are not able to make every pizza exactly this size. The manager has calculated that the size of the pizzas is normally distributed with a mean of 16 inch and a standard deviation of 0.8 inch.

a) What is the probability (chance) that in the random sample of two pizzas the average size is less than 15.5 inches?

b) What is the probability (chance) that in the random sample of four pizzas the average size is less than 15.5 inches?

3. The study found that 55% of British firms experienced a cyber-attack in the past year.

a) What are the expected value and standard error of the sample proportion derived from a random sample of 100 firms?

b) In a random sample of 100 firms, what is the probability that the sample proportion is greater than 0.57?