Suppose the dentists at the Eastin Center for Modern Dentistry in Coeur D’Alene, Idaho, never see a patient on time. The amount of time (in minutes) past the appointment time a random patient must wait to see a dentist has an exponential distribution with l 5 0.01. Suppose a patient is selected at random, and the appointment time has passed.
a. What is the probability that the dentist will see the patient within five minutes after the appointment time? Write a Solution Trail for this problem.
b. Find the probability that the dentist will see the patient between 10 and 20 minutes after the appointment time.
c. Find the probability that the patient will have to wait at least 30 minutes past the appointment time.
In Columbia, South Carolina, on a randomly selected Friday night between 9:00 p.m. and 2:00 a.m., the time (in minutes) between calls to a 911 dispatcher has an exponential distribution with l 5 0.125. Suppose a Friday evening in Columbia is selected at random.
a. If a 911 call is taken at 10:07 p.m., what is the probability that the next call will occur before 10:30 p.m.?
b. If a 911 call is taken at 11:30 p.m., what is the probability that the next call will occur after 11:45 p.m.?
c. Find the mean, variance, and standard deviation for the time between 911 calls.
d. Find a value t such that if a 911 call is received between 9:00 p.m. and 2:00 a.m., then the probability that the next 911 call will occur more than t minutes later is 0.75.