A boat capsized and sank in a lake. Based on an assumption of a mean weight of 1

Question

A boat capsized and sank in a lake. Based on an assumption of a mean weight of 148 lb, the boat was rated to carry 70 passengers (so the load limit was 10,360 Ib). After the boat sank, the assumed mean weight for similar boats was changed from 148 lb to 174 lb. Complete parts a and b below. a. Assume that a similar boat is loaded with 70 passengers, and assume that the weights of people are normally distributed with a mean of 180.2 lb and a standard deviation of 37.3 lb. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 148 lb. The probability is 1 (Round to four decimal places as needed.) b. The boat was later rated to carry only 13 passengers, and the load limit was changed to 2,262 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 174 (so that their total weight is greater than the maximum capacity of 2,262 lb). The probability is (Round to four decimal places as needed.) Enter your answer in the answer box and then click Check Answer Clear All Check Answer remainino javascriptdoExercise(3);

Explanation / Answer

b)

=180.2

=37.3

n=13

x=174

z=(x-)/(/n)

=(174-180.2)/(37.3/13)

=-6.2/10.34516

=-0.5993

P(x>174 ) =P(z>-0.5993)

=1-P(z<-0.5993)

=1-0.2745

=0.7255

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