It is widely known that many drivers on interstate highways in the United States do not observe the posted speed limit. Assume that the actual rates of speed driven by U.S. motorists are normally distributed with mean μ mph and standard deviation 5 mph.
Given this information, answer each of the following independent questions.
(Hint: Use Goal Seek in parts a and b, and use the Solver add-in with no objective in part c. Solver is usually used to optimize, but it can also be used to solve equations with multiple unknowns.)
a. If 40% of all U.S. drivers are observed traveling at 65 mph or more, what is the mean μ?
b. If 25% of all U.S. drivers are observed traveling at 50 mph or less, what is the mean μ?
c. Suppose now that the mean μ and standard deviation σ of this distribution are both unknown. Furthermore, it is observed that 40% of all U.S. drivers travel at less than 55 mph and 10% of all U.S. drivers travel at more than 70 mph. What must μ and σ be?