A boat capsized and sank in a lake. Based on an assumption of a mean weight of 142 ​lb, the boat was rated to carry 50 passengers​ (so the load limit was 7,100 lb). After the boat​ sank, the assumed mean weight for similar boats was changed from 142 lb to 175lb.    a. Assume that a similar boat is loaded with 50 passengers, and assume that the weights of people are normally distributed with a mean of 179.6 lb and a standard deviation of 36.7lb. Find the probability that the boat is overloaded because the 50 passengers have a mean weight greater than 142lb.   the probability is ???

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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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 142 ​lb, the boat was rated to carry 50 passengers​ (so the load limit was 7,100 lb). After the boat​ sank, the assumed mean weight for similar boats was changed from 142 lb to 175lb. 
 
a. Assume that a similar boat is loaded with 50 passengers, and assume that the weights of people are normally distributed with a mean of 179.6 lb and a standard deviation of 36.7lb. Find the probability that the boat is overloaded because the 50 passengers have a mean weight greater than 142lb.
 
the probability is ???
A boat capsized and sank in a lake. Based on an assumption of a mean weight of
142 Ib, the boat was rated to carry 50 passengers (so the load limit was 7,100
Ib). After the boat sank, the assumed mean weight for similar boats was changed
from 142 Ib to 175 lb. Complete parts a and b below.
a. Assume that a similar boat is loaded with 50 passengers, and assume that the
weights of people are normally distributed with a mean of 179.6 Ib and a
standard deviation of 36.7 Ib. Find the probability that the boat is overloaded
because the 50 passengers have a mean weight greater than 142 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 142 Ib, the boat was rated to carry 50 passengers (so the load limit was 7,100 Ib). After the boat sank, the assumed mean weight for similar boats was changed from 142 Ib to 175 lb. Complete parts a and b below. a. Assume that a similar boat is loaded with 50 passengers, and assume that the weights of people are normally distributed with a mean of 179.6 Ib and a standard deviation of 36.7 Ib. Find the probability that the boat is overloaded because the 50 passengers have a mean weight greater than 142 Ib. The probability is. (Round to four decimal places as needed.)
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