Question

a mathxl.com Turn O Statistics Summer 2019 Section 9 Nancy Serrano Always for Micr Homework: Homework 5 HW Score: 26.67 % , 1.33 of 2 of 5 (2 complete) core: 0 of 1 pt 5.4.18-T Question Help A boat capsized and sank in a lake. Based on an assumption of a mean weight of 130 lb, the boat was rated to carry 60 passengers (so the load limit was 7,800 lb) After the boat sank, the assumed mean weight for similar boats was changed from 130 lb to 170 lb. Complete parts a and b below. a. Assume that a similar boat is loaded with 60 passengers, and assume that the weights of people are normally distributed witha mean of 180.5 lb and a standard deviation of 38.4 lb. Find the probability that the boat is overloaded because the 60 passengers have a mean weight greater than 130 lb. The probability is (Round to four decimal places as needed.) tis mn 400 Enter your answer in the answer box and then click Check Answer. is S Check Annwr Ciogr All

Answer 1

Mean = 180.5

Standard Deviation = 38.4

Now, we need to calculate probability of Mean greater than 130

Z = (x- $\small \mu$) / $\small \sigma$ = (130 - 180.5) / 38.4 = -50.5 / 38.4 = -1.31

Now ,P(X>-1.31) = 1 - P(X<-1.31) = 1 - 0.0968 = 90.32%

Therefore, Probability that mean weight will be greater than 130lbs = 90.32%