7.33 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 Columbus 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.

e. Define a new random variable t 5 d1 1 d2. Find the probability distribution of t.

f. For each of the following statements, indicate if the statement is true or false and provide statistical evidence to support your answer.

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i. E(t) = E(d) + E(d) (Hint: E(t) is the ex- pected value of t and another way of denoting the mean of t.)