You work as a Quality Control Technician for a manufacturer of kitchen countertops and your job is to randomly sample countertops to ensure product consistency. The machining time for each countertop is, on average, 20.2 seconds for a particular machine centre.

1/

If it is known that the standard deviation is 4 seconds, what is the probability that the sample mean will lie between 19.2 seconds and 21.2 seconds in a sample of 4 countertops?

2/

If it is known that the standard deviation is 4 seconds, what is the probability that the sample mean will lie between 19.2 seconds and 21.2 seconds in a sample of 16 countertops?

3/

Based on your answers to question 1) and 2), why are the confidence intervals different? Explain what happened when the sample size increased from 4 to 16.