Complete parts a and b below. Assume that a similar boat is loaded with 60 passengers, and assume that the weights of people are normally distributed with a mean of 178.3 lb and a standard deviation of 39.1 lb. Find the probability that the boat is overloaded because the 60 passengers have a mean weight greater than 130 lb. The boat was later rated to carry only ​16 passengers, and the load limit was changed to 2,736 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 171 ​(so that their total weight is greater than the maximum capacity of  2736 ​lb).

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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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 to171 lb. Complete parts a and b below.

Assume that a similar boat is loaded with 60 passengers, and assume that the weights of people are normally distributed with a mean of 178.3 lb and a standard deviation of 39.1 lb. Find the probability that the boat is overloaded because the 60 passengers have a mean weight greater than 130 lb.

The boat was later rated to carry only ​16 passengers, and the load limit was changed to 2,736 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 171 ​(so that their total weight is greater than the maximum capacity of  2736 ​lb).

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