A boat capsized and sank in a lake. Based on an assumption of a mean weight of 143 lb, the boat was rated to carry 70 passengers (so the load limit was 10,010 Ib). After the boat sank, the assumed mean weight for similar boats was changed from 143 lb to 171 Ib. 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 178.9 lb and a standard deviation of 35.8 lb. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 143 lb. The probability is (Round to four decimal places as needed.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 14PPS
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A boat capsized and sank in a lake. Based on an assumption of a mean weight of 143 lb, the boat was rated to carry 70 passengers (so the load limit was 10,010 lb). After the boat sank, the assumed mean weight for
similar boats was changed from 143 lb to 171 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 178.9 lb and a standard deviation of 35.8 lb. Find the probability that the boat
is overloaded because the 70 passengers have a mean weight greater than 143 Ib.
The probability is
(Round to four decimal places as needed.)
Transcribed Image Text:A boat capsized and sank in a lake. Based on an assumption of a mean weight of 143 lb, the boat was rated to carry 70 passengers (so the load limit was 10,010 lb). After the boat sank, the assumed mean weight for similar boats was changed from 143 lb to 171 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 178.9 lb and a standard deviation of 35.8 lb. Find the probability that the boat is overloaded because the 70 passengers have a mean weight greater than 143 Ib. The probability is (Round to four decimal places as needed.)
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