a) The mean number of cargo ships that arrive at a port is 3 per day. The port has staff and facilities to handle up to 6 ships in a day. Using the Poisson distribution, find the probability that, on a given day,

i. five ships will arrive;

ii. too many cargo ships will arrive.

b) The following represents a random sample of the amounts of carbohydrates (in grams) for thirty sandwiches from a fast food restaurant:

33 30 31 33 37 39 40 45 37 37 62 61 59 43 40

44 49 59 51 62 55 66 39 35 27 34 27 33 29 29

Find, by hand, a 95% condence interval for the mean amount of carbohydrates in sandwiches at this particular restaurant.