Answered: A local micro-brewery dispenses its…

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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Question

A local micro-brewery dispenses its various non-alcoholic and alcoholic products into 473 millilitre (mL)
glasses - the amount of a pint. Not all the micro-brewery’s servers are consistent when filling “one pint”
glasses with product. The amount of product filled in 473 ml glasses (there is a line on each glass indicating
when to stop filling) various from one server to the next. This server-to-server variation of the amount of
product dispensed can be modeled by the Normal probability model with a mean of 471 mL and a standard
deviation of 1.5 mL.
(a) You have ordered a “pint” of something at this micro-brewery. Compute the probability that you are
given between 470 mL and 472 mL.
(b) Compute the 90th percentile, x90. Then, interpret its meaning in the context of these data.
(c) An “overfill” occurs when the server has provided you with more than 473 mL of product. Compute
the chance that the glass of product received in part (a) was “overfilled”?
(d) You randomly pick n = 30 “pints”. Compute the chance that between 3 and 6, inclusive, will be
overfilled.

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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