SmartDoor Design is a new company that is designing wifi-enabled doors that will automatically lock and unlock when you have your phone and are near your door. In considering the design of the door, the design team obtains heights of the U.S. adult population. They find the mean height is 66 inches with a standard deviation of 4 inches. For each part, find the standard normal transformation as part of your solution, use R to find the probability (provide the line of code used), and provide a summary statement of the findings. a) If the design team makes the door 58 inches high, what percentage of the adult population would hit their head if they do not duck when going through the door? b) If the design team makes the door 70 inches high, what percentage of the population would be able to use the door successfully? What percentage would need to duck? c) If the design team makes the door 80 inches high, what percentage of the population would be able to use the door successfully? What percentage would need to duck