Answer to Question #329907 in Statistics and Probability for azi

Question

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  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 ?

b. If 25% of all U.S. drivers are observed traveling at

50 mph or less, what is the mean ?

c. Suppose now that the mean  and standard deviation

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  and  be?

Answer 1

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