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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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.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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