An automatic puck shooting machine is a device that fires hockey pucks at specified speeds. The machine's manufacturer, Puck Chuck, constructed the device so that there was little variance in the velocities of the projectiles. For example, if a machine was to be set at a mean output of 90 miles perhour (mph), its standard deviation would remain 4 mph. Assuming that actual speeds of the device are normally distributed, please answer the following questions about a machine set to shoot pucks at 90 mph:
a) What is the probability of a puck being shot at speeds in between 82 and 96 mph?
b) If Puck Chuck wanted to reset the machine so that only 17 in 1000 pucks would have velocities of less than 80 mph, what would the mean output of the machine be set to?