Pritchard Phillips

08/30/2024 · High School

A boat capsized and sank in a lake. Based on an assumption of a mean weight of 144 lb , the boat was rated to carry 50 passengers (so the load limit was \( 7,200 \mathrm{lb} \) ). After the boat sank, the assumed mean weight for similar boats was changed from 144 lb to 170 lb . Complete parts a and b below. a. Assume that a similar boat is loaded with 50 passengers, and assume that the weights of people are normally distributed with a mean of 181.3 lb and a standard deviation of 39.6 lb . Find the probability that the boat is overloaded because the 50 passengers have a mean weight greater than 144 lb . The probability is 1 . (Round to four decimal places as needed.) b. The boat was later rated to carry only 14 passengers, and the load limit was changed to \( 2,380 \mathrm{lb} \). Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 170 (so that their total weight is greater than the maximum capacity of \( 2,380 \mathrm{lb} \) ). The probability is \( \square \). (Round to four decimal places as needed.)