Answered: During its manufacturing process,…

Name: During its manufacturing process, Fantra fills its 20 fl oz bottles us
Uploaded: 2024-03-20T07:07:12.000Z
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Description: During its manufacturing process, Fantra fills its 20 fl oz bottles using an automated filling machine. This machine is not perfect and will not always fill each bottle with exactly 20 fl oz of soft drink. The amount of soft drink poured into each bo

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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During its manufacturing process, Fantra fills its 20 fl oz bottles using an automated filling machine. This machine is not perfect and will not always fill each bottle with exactly 20 fl oz of soft drink. The amount of soft drink poured into each bottle follows a normal distribution with mean 20 fl oz and standard deviation 0.17 fl oz.

The Fantra quality testing department has just carried out a routine check on the average amount of soft drink poured into each bottle. A sample of 25 bottles were randomly selected and the amount of soft drink in each bottle was measured. The mean amount of soft drink in each bottle was calculated to be 19.90 fl oz. The Fantra Chief Executive Officer believes that such a low mean is not possible and a mistake must have been made.

Calculate the probability of obtaining a sample mean below 19.90 fl oz. Give your answer as a decimal to 4 decimal places.

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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