Refer to Exercise 52.

a. Assume that B and W are independent random variables. Explain what this means in context.

b. Calculate and interpret the standard deviation of the difference D (Bus − Walk) in the time it would take Sulé to get to work on a randomly selected day.

c. From the information given, can you find the probability that it will take Sulé longer to get to work on the bus than if he walks on a randomly selected day? Explain why or why not.

Exercise 52.

Sulé’s job is just a few bus stops away from his house. While it can be faster to take the bus to work than to walk, the travel time is more variable due to traffic. The commute time B if Sulé takes the bus to work on a randomly selected day has mean 12 minutes and standard deviation 4 minutes. The commute time W if Sulé walks to work on a randomly selected day has mean 16 minutes and standard deviation 1 minute. Calculate and interpret the mean of the difference D = B − W in the time it would take Sulé to get to work on a randomly selected day.