A boat capsized and sank in a lake. Based on an assumption of a mean weight of 150​lb, the boat was rated to carry 70 passengers​ (so the load limit was 10 comma 500​lb). After the boat​ sank, the assumed mean weight for similar boats was changed from 150lb to 173lb. assume that a similar boat is loaded with 70​passengers, and assume that the weights of people are normally distributed with a mean of 178.3lb and a standard deviation of 39.7 lb. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 150 lb. The probability is1.    a. The boat was later rated to carry only 16 ​passengers, and the load limit was changed to 2 comma 768 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 173 ​(so that their total weight is greater than the maximum capacity of 2 comma 768 ​lb). The probability is ​(Round to four decimal places as​ needed.)

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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A boat capsized and sank in a lake. Based on an assumption of a mean weight of 150​lb, the boat was rated to carry 70 passengers​ (so the load limit was 10 comma 500​lb). After the boat​ sank, the assumed mean weight for similar boats was changed from 150lb to 173lb.

assume that a similar boat is loaded with 70​passengers, and assume that the weights of people are normally distributed with a mean of 178.3lb and a standard deviation of 39.7 lb. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 150 lb. The probability is1. 

 

a. The boat was later rated to carry only 16 ​passengers, and the load limit was changed to 2 comma 768 lb. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 173 ​(so that their total weight is greater than the maximum capacity of 2 comma 768 ​lb).

The probability is
​(Round to four decimal places as​ needed.)
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