Psychology and Human Behavior 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