1 A water taxi sank after capsizing in a squall in Baltimore Inner Harbor in March, 2004. In certifying the boat, the US Coast Guard had estimated its maximum safe operating load to be 3500 lb and, based on human weight data collected in 1942, determined that 25 was the maximum total number of passengers and crew that could be safely carried. Of the 25 people aboard at the time of the accident, 16 were injured and five died, including a woman and her daughter from Vineland, NJ. The weight of passengers was later found to have been 4210 lb. Calculate

(i) the mean passenger weight assumed by the USCG through its certification procedure and

(ii) the actual mean passenger weight at the time of the capsize. If the weights of adult males in the USA are approximately Normally distributed as N(172 lb, 29 lb),

(iii) calculate the probability that the weight of a single male passenger, selected at random, exceeds the actual mean passenger weight on the day of the accident. Assuming a worst case in which all 25 passengers are adult men,

(iv) calculate the probability that the mean passenger weight would exceed the maximum safe load as determined by the USCG. Two months after the accident, the USCG ordered the operator of the water taxi to reduce passenger load on all its craft by "about 25%".

(v) Calculate the new maximum number permitted to be carried and

(vi) calculate the probability that the mean passenger weight would still exceed the permitted maximum safe load, again assuming all passengers to be adult men