At a local pizza parlor the owner is concerned that he may be losing profits due to the amount of toppings his employees are putting on the pizzas. One of the most popular pies that this parlor sells is the smoked salmon pizza which comes with salmon, cheese, onion and capers. Due to its high cost, the employees are only supposed to put 8 pieces of salmon on an 8 slice medium pizza. However, the owner is concerned his staff isn't following this rule. To make sure they are, the owner decides to count the number of pieces of salmon on the next 40 pizzas and finds the average amount of salmon to be 11 pieces. Assume that the population pizza is normally distributed with a standard deviation of 2 pieces of salmon.
A. Construct a 90% two sided confidence interval for the true number of pieces of salmon on the pizzas.
B. Are the owner's standards for pizza making met at this confidence interval? Why?
C. Construct a 95% upper confidence interval for the true number of pieces of salmon on the pizzas.