A maternity ward has an average of 4500 birth per year that oeeur randomly. During the night shift 11pm to 7am , the number of deliveries is, on average, 1,500, is. the average per night is A = 1,500 f 365 = 4.10%. Let the random variable X denote the number of biris per night shift and assume X has a Poisson distribution, determine the probability that there are: (a) less than txvo deliveries per night shift; and (b) more than eight deliveries per night shift. In addition to that, determine: (o) for how many night shifts per year can we expect to have more than 8 deliveries; and (d) discuss what invalidates the use of a Poisson distribution here