Answer for question B) from the word bank Pregunta 9A population of 2 liter bottles of cola is known to have a mean fill-weight of 2.06 liters and a standard deviation of 0.02liters.Calculate:H+o = ( _2.042.08H± 20 = ( 2.022.10H±30 = ( 2.002.12(A) If the population is knownbe bell-shaped, then we can conclude that between 0 and 11.1% of the bottles willcontain less than 2 liters.(B) If the shape of the population isunknown, and you cannot assume that it is bell-shaped, then we can conclude thatbetween 0 and% of the bottles will contain less than 2 liters.Banco de palabras:0.152.0211.15.552.122.040.32.002.102.08

Answered: er for question B) from the wor

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

Answer for question B) from the word bank

Pregunta 9
A population of 2 liter bottles of cola is known to have a mean fill-weight of 2.06 liters and a standard deviation of 0.02
liters.
Calculate:
H+o = ( _2.04
2.08
H± 20 = ( 2.02
2.10
H±30 = ( 2.00
2.12
(A) If the population is known
be bell-shaped, then we can conclude that between 0 and 11.1
% of the bottles will
contain less than 2 liters.
(B) If the shape of the population isunknown, and you cannot assume that it is bell-shaped, then we can conclude that
between 0 and
% of the bottles will contain less than 2 liters.
Banco de palabras:
0.15
2.02
11.1
5.55
2.12
2.04
0.3
2.00
2.10
2.08

Expert Solution

Step 1

NOTE: As mentioned by the student, I have to attempt only the B part. Hence, I am solving part B) only.

B).

We know that the Empirical rule is valid only for Normal distributions, which states that with mean $μ$ and standard deviation $σ$ :

68% of the data lies within 1 standard deviation limits, i.e, $μ \pm σ$ .
95% of the data lies within 2 standard deviation limits, i.e, $μ \pm 2 σ$ .
99.7% of the data lies within 3 standard deviation limits, i.e, $μ \pm 3 σ$ .

The case of Normal distribution is used in the part A). In this case, we are told that the distribution is not bell shaped, i.e, it is NOT NORMAL.

In such a case, we will use Chebyshev's Inequality.
Chebyshev's Inequality states that the proportion f data values that lies within given number of standard deviations is obtained by $P \geq 1 - \frac{1}{k^{2}}$ , where P=proportion of data values to be calculated and k=Number of standard deviations provided.