Answered: part a: The times for a particular…

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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part a: The times for a particular journey during rush hour in a large city have to mean 24.4 minutes and standard deviation 9.9 minutes. Using the Central limit theorem: Find the probability that the mean time taken for a random sample of 70 of the time for this journey is more than 25 minutes.

part b:

The weights, in grams, of bags of cocoa beans, are known to have a standard deviation of 4 grams. A random sample of bags is weighted with the following results:

746, 748, 754, 752, 747, 756, 751, 740, 759, 755

Calculate a 96% confidence interval for the mean weight of a bag of cocoa beans

part c:

A factory produces a particular electrical component and on average 0.97 is correctly. In a batch of 120 components taken at random, using the Binomial probability distribution, what is the probability that exactly 2 components are faulty?

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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