An airline is charged by an airport based upon the total taxi-time that an airplane spends to take off and land. Suppose taxi time, a, at airport A is normally distributed with mean of 27 minutes and standard deviation 8 minutes; taxi time, b, at airport B is normally distributed with mean of 39 minutes and standard deviation 12 minutes; taxi time, c, at airport C is normally distributed with mean of minutes and standard deviation 10 minutes. JJ Airlines has a plane flying to airport A, airport B, and airport C on Sunday. Airport A charges $131 per minute of taxi time; airport B charges $150 per minute of taxi time; airport c charges $200 per minute of taxi time. I X = total amount of taxi time in minutes for the JJ plane. Let W = total taxi charges for the JJ plane. X is defined as X = a + b + c. W 131a + 150b + 200c. Note that a, b, and c are independent of one another. a) Calculate the expected value of X. [ b) Calculate the standard deviation of X.

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