**Understanding the Impact of Average Passenger Weight on Boat Safety**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.**Problem 1:**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.)*---**Explanation for the Educational Website:****Context:** This exercise explores the real-life implications of statistical assumptions. It helps understand how the average weight of passengers affects boat safety and load capacity.**Instructions:** In problem 1, you need to determine the probability that a boat is overloaded under given conditions. The task involves using the concepts of normal distribution, mean, and standard deviation to assess risk and safety.**Learning Objectives:**1. Understand the importance of correct assumptions in safety assessments.2. Apply statistical methods to calculate probabilities relevant to real-world scenarios.3. Recognize how changes in assumed averages can impact safety regulations.Please proceed by calculating the given probability to enhance your learning and understanding of statistical application in safety measures.

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Description: **Understanding the Impact of Average Passenger Weight on Boat Safety**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

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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 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.)

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.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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**Understanding the Impact of Average Passenger Weight on Boat Safety**

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.

**Problem 1:**

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.)*

---

**Explanation for the Educational Website:**

**Context:** This exercise explores the real-life implications of statistical assumptions. It helps understand how the average weight of passengers affects boat safety and load capacity.

**Instructions:** In problem 1, you need to determine the probability that a boat is overloaded under given conditions. The task involves using the concepts of normal distribution, mean, and standard deviation to assess risk and safety.

**Learning Objectives:**
1. Understand the importance of correct assumptions in safety assessments.
2. Apply statistical methods to calculate probabilities relevant to real-world scenarios.
3. Recognize how changes in assumed averages can impact safety regulations.

Please proceed by calculating the given probability to enhance your learning and understanding of statistical application in safety measures.

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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. 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____