Explanation please.

The Poisson Distribution The Poisson Distribution is a Discrete Probability Distribution that is commonly applied when a series of trials! experiments occur over an interval. (The number of meteors per hour; hailstones per acre). Here, the average timefdistancer'etc. between each event must be known. This type of distribution may be used if the following conditions apply: I Each event is independent. - The average rate is constant (events per interval). - Two events cannot occur at the same time. Apply the Poisson Distribution to a scenario. On average, a baking student accidentally drops three pieces of egg shell into the batter of every two cakes made. The conditions of a Poisson Distribution are met: I The baking of a cake does not affect the outcome of any other cake. (independent events) 3 - The average rate is constant: 3 pieces per 2 cakes (rate = E = 1.5) - Baking (and dropping eggshells) is a sequential process. (Two events cannot occur at the same time) Use the scenario above to determine the expected value (p) and selected probabilities below. You may wish to use the Poisson Distribution Calculator hosted by the University of Iowa's Department of Mathematical Sciences. Remember: the formatting of this calculator may vary slightly from what is used in class. (link: Poisson Distribution Calculator 57'} a. On average, how many cg shells do you expect to be in a single cake? p: = l l (decimal answers only) b. If a single cake is bought, what is the probability of finding 0 egg shell pieces in it? P(X = 0) = I (include four decimal places) c. If a single cake is bought, what is the probability of finding more than two egg shell pieces in it? P(X > 2) = I (include four decimal places)