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 50 passengers (so the load limit was 7,500 lb). After the boat sank, the assumed mean weight for similar boats was changed from 150 lb to 172 Ib. 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 177.7 Ib and a standard deviation of 40.3 lb. Find the probability that the boat is overloaded because the 50 passengers have a mean weight greater than 150 lb. The probability is (Round to four decimal places as needed.)

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 50 passengers (so the load limit was 7,500 lb). After the boat sank, the assumed mean weight for similar boats was changed from 150 lb to 172 Ib. 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 177.7 Ib and a standard deviation of 40.3 lb. Find the probability that the boat is overloaded because the 50 passengers have a mean weight greater than 150 lb. The probability is (Round to four decimal places as needed.)

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Chapter1: Combinatorial Analysis

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Question

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 50 passengers (so the load limit was 7,500 lb). After the boat sank, the assumed mean
weight for similar boats was changed from 150 lb to 172 Ib. 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 177.7 Ib and a standard deviation of 40.3 lb. Find the probability that
the boat is overloaded because the 50 passengers have a mean weight greater than 150 lb.
The probability is:
(Round to four decimal places as needed.)

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