Records kept at Boston’s Brigham Hospital show an average of 1.4 maternity patients per hour check in during the 8 P.M. to 2 A.M. shift (that is, λ = 1.4 check-ins per hour). Assume that maternity patient check-ins meet all the Poisson conditions.
a. How likely is it that less than a half-hour will elapse between one check-in and the next?
b. How likely is it that more than two hours will elapse between successive check-ins?
c. It is now 10:30 P.M. How likely is it that no more than 20 minutes will elapse before the next check-in?
d. How likely is it that between 30 minutes and 45 minutes will elapse before the next maternity patient checks in?