Question

mean weight for nimlar boats was changed trom 149 ib to 175 ib Complete parts a and b below. a. Assume that a similar boat is losded weh 60 passengees, and astume that the weights of people are normally datrituted with a mbah of ta2.1 ib and a standerd deviaton of ag. 7 ib. Find Bet probablity that the bost is cverloaded because the 60 possengers have a mean weight greater than 149 ib. The probsbach is (Round to four deoinal places as needed)

Answer 1

The question entails calculating the probability that 60 passengers on a boat exceed an average weight of 149 pounds and whether it is a safety concern if 20 men exceed a total weight of 3,500 pounds. It involves understanding normal distribution and using Z-scores for probability calculations.

Step-by-step explanation:

Part A of the question involves calculating the probability that the mean weight of 60 passengers on a boat is greater than 149 pounds, assuming the weights are normally distributed with a mean of 162.1 pounds and a standard deviation of 29.7 pounds. To find this probability, we would use the standard normal distribution (Z-score). However, the result for the probability calculation was not provided in the question.

Part B inquires whether it is a safety concern if the sum weight of 20 men is greater than 3,500 pounds, which implies we need to consider the safety limits for water taxis. The answer to this would depend on the resultant probability from part A, and whether that probability is sufficiently high to be of concern. When considering 20 men with an average weight of 172 pounds and a standard deviation of 29 pounds, using the central limit theorem can help us determine the probability that their total weight exceeds 3,600 pounds; if this is likely, then it may translate to a safety concern for the boat in question as well.