Prior to placing an order, the amount of time (in minutes) that a driver waits in line at a Starbucks drive-thru follows an exponential distribution with a probability density function of f(x) = 0.19e−0.19x.
a. What is the mean waiting time that a driver faces prior to placing an order?
b. What is the probability that a driver spends more than the average time before placing an order? (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)
c. What is the probability that a driver spends more than 12 minutes before placing an order? (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)
d. What is the probability that a driver spends between 6 and 11 minutes before placing an order? (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)