Solve the following question: suppose small aircraft arrive at a certain airport according to a poisson process with rate a = 8 per hour. a. what is the probability that exactly 6 small aircraft arrive during a 1-hour period? at least 6? at least 10? b. what are the expected value and standard deviation of the number of small aircraft that arrive during a 90-min period? c. what is the probability that at least 20 small aircraft arrive during a 2.5-hour period? that at most 10 arrive during this period?

Brittany has designed four different birdcages, each with the same volume: a square pyramid, a cylinder, a cone, and a sphere. the zoo wants to use one of brittany’s designs but plans to change the volume of the cage. find the design change that would result in the birdcage with the greatest volume. a.) increase the area of the base of the square pyramid by a factor of ten. b.) increase the height of the cylinder by a factor of ten. c.) increase the radius of the cone by a factor of ten. d.) increase the radius of a sphere by a factor of ten.