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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.

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.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
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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.

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Comment: As per the our comapny guidelines we are supposed to answer only three subparts. Kindly repost other parts in the next question.

Let X be 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.

X tilde N left parenthesis mu equals 471 comma space sigma equals 1.5 right parenthesis

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