Children laugh an average of 16.67 times an hour and adults laugh an average of 0.6667 times an hour. Let X be the number of times a child laughs in an hour, and let Y be the number of times an adult laughs in an hour.
a. What is the probability that a child will laugh exactly 20 times in the next hour? What is the corresponding probability that an adult will laugh exactly 20 times in the next hour?
b. Why are these situations Poisson?
c. Given that an adult laughs more than 1 time in an hour, what is the probability that the adult laughs at least 3 times in the next hour?
d. Given that an adult laughs less than 3 times in the next hour, what is the probability that the adult laughs once or less?
e. Show the labeled graph of the mass for adults in this story.
f. Show the labeled graph of the mass for children in this story.
g. Show the labeled graph of the CDF for adults in this story.
h. Show the labeled graph of the CDF for children in this story.
(The graphs for e and g should look relatively clear after just a few points, t perhaps two dozen points will be needed to get a good understanding of the graphs for f and h. A graphing calculator or computer might make the graphs f and h quicker to computer.)