P Do Homework Section 64 - Google Chromemathxl.com/Student/PlayerHomework.aspx?homeworkld%3D587793988&questionld%3D1&flushed%=false&cld%3D635961...Math 1103-4 Spring 2021Homework: Section 6.4SaveScore: 0 of 1 pt4 of 4 (0 complete)HW Score: 0%, 0 of 4 pts6.4.18-TQuestion Help ▼A boat capsized and sank in a lake. Based on an assumption of a mean weight of 131 lb, the boat was rated to carry 60passengers (so the load limit was 7,860 lb). After the boat sank, the assumed mean weight for similar boats was changed from131 lb to 171 Ib. Complete parts a and b below.a. Assume that a similar boat is loaded with 60 passengers, and assume that the weights of people are normally distributedwith a mean of 177.4 lb and a standard deviation of 39.3 lb. Find the probability that the boat is overloaded because the 60passengers have a mean weight greater than 131 lb.The probability is(Round to four decimal places as needed.)Enter your answer in the answer box and then click Check Answer.2 partsremainingClear AllCheck AnswerO.Type here to searcha%23II P Do Homework- Section 6.4-Google Chromemathxl.com/Student/PlayerHomework.aspx?homeworkld%3D587793988&questionld%31&flushed%3Dfalse&cld%3D635961...Math 1103-4 Spring 2021Homework: Section 6.4SaveScore: 0 of 1 pt1 of 4 (0 complete)HW Score: 0%, 0 of 4 pts6.4.9Question Help ▼An elevator has a placard stating that the maximum capacity is 1352 Ib-8 passengers. So, 8 adult male passengers can havea mean weight of up to 1352 /8= 169 pounds. If the elevator is loaded with 8 adult male passengers, find the probability that itis overloaded because they have a mean weight greater than 169 lb. (Assume that weights of males are normally distributedwith a mean of 172 lb and a standard deviation of 32 lb.) Does this elevator appear to be safe?The probability the elevator is overloaded is.(Round to four decimal places as needed.)Enter your answer in the answer box and then click Check Answer.1 partremainingClear AllCheck AnswerO Type here to search0 耳

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Answered: A boat capsized and sank in a lake.…

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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Given Information:

Mean $μ = 177.4$ lb

Standard deviation $σ = 39.3$ lb

Sample size $n = 60$

To find the probability that the boat is overloaded because the 60 passengers have a mean greater than 131 lb:

Z-score is a measure which indicates how many standard deviations away, a data value is, from the mean. It is given by the formula:

$z = \frac{\bar{x} - μ_{\bar{x}}}{σ_{\bar{x}}}$

Based on the concept of central limit theorem:

If a sample of size $n > 30$ is drawn from a normal population with mean $μ$ and standard deviation $σ$ , then the sampling distribution of sample mean $\bar{x}$ is approximately normally distributed with mean $μ_{\bar{x}} = μ$ and standard deviation $σ_{\bar{x}} = \frac{σ}{\sqrt{n}}$

So, the mean of sample mean is $μ_{\bar{x}} = μ$ = 177.4

Standard deviation of sample mean is $σ_{\bar{x}} = \frac{39.3}{\sqrt{60}} = 5.073608184$

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