Suppose a company produces guidance systems for hot air balloons.  The company makes compasses with errors (measured in degrees) that are standard normally distributed. Negative values mean the desired direction is to the navigator’s left and positive values indicate the desired direction is to the right.  An error of –2.45 means the navigator needs to turn left 2.45 degrees from the current direction.

1. What is the probability a reading will be off by more that 1.88 degrees (left or right)?  Clearly label and shade a diagram that one would use to solve this problem.  Show any additional work below and circle your answer.

2. The pilot of the balloon is currently headed in what she thinks is the proper direction.  However if the correct direction is more than 1.88 degrees to the left, she will end up over a hostile country that she is trying to avoid.  If there is a probability of 0.10 or more that she will end up over this country, she will change directions to reduce the risk of dealing with the hostile territory.  What should she do?  Stay on course___   Change direction___
Show your work and explain your decision.

3. Suppose she stays on the same course (disregard your decision in Question 2).  If she is wrong, she figures the fines and lost time will cost her about $2000 that she did not intend to spend on the trip.  What is her expected loss, if she loses nothing if the direction is correct?  Show your work.

4. Suppose she considers turning so that she will avoid the hostile country unless the correct direction is more than 2.88 degrees to the left.  However, this turn means that it will take her longer to arrive and cost her an extra $750 in fuel and landing fees.  Given your result in Question 3, what should she do to minimize costs?