The states of Ohio, Iowa, and Idaho are often confused, probably because the names sound so similar. Each year, the State Tourism Directors of these three states drive to a meeting in one of the state capitals to discuss strategies for attracting tourists to their states so that the states will become better known. The location of the meeting is selected at random from the three state capitals. The shortest highway distance from Boise, Idaho to Columbus, Ohio passes through Des Moines, Iowa. The highway distance from Boise to Des Moines is 1350 miles, and the distance from Des Moines to Colum- bus is 650 miles. Let d1 represent the driving distance from Columbus to the meeting, with d2 and d3 representing the distances from Des Moines and Boise, respectively.
a. Find the probability distribution of d1 and display it in a table.
b. What is the expected value of d1?
c. What is the value of the standard deviation of d1?
d. Consider the probability distributions of d2 and d3. Is either probability distribution the same as the probability distribution of d1? Justify your answer.