Answered: A company produces a range of snack…

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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A company produces a range of snack foods, including cookies. The cookies are produced so that the weight of each cookie is normally distributed with a mean of 25g and a standard deviation of 0.8g. The cookies are then packaged in groups of 12, with an advertised net weight of 295g. The quality control officer for the company is looking at the likelihood of packs of cookies being under the advertised weight. His interest therefore shifts to the mean weight of cookies in a sample of 12, which will be denoted X .
i) State the distribution of the mean of a sample of 12 randomly selected cookies (that is, X ) and give the value(s) of its parameter(s).
ii) Determine the mean weight of cookies in a pack in order for the total contents to be 295g. Hence determine the probability that a randomly selected pack of cookies has a weight that is below the advertised weight.

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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